`sum_(n=1)^oo (-1)^n/e^n` Determine the convergence or divergence of the series.

Recall the Ratio test determines the limit as:

`lim_(n-gtoo)|a_(n+1)/a_n| = L`

 Then ,we follow the conditions:

a) `L lt1` then the series is absolutely convergent

b) `Lgt1` then the series is divergent.

c) `L=1` or does not exist  then the test is inconclusive. The series may be divergent, conditionally convergent, or absolutely convergent.

We may apply the Ratio Test to determine the convergence or divergence of the series `sum_(n=1)^oo (-1)^n/e^n` .

For the...

Recall the Ratio test determines the limit as:

`lim_(n-gtoo)|a_(n+1)/a_n| = L`

 Then ,we follow the conditions:

a) `L lt1` then the series is absolutely convergent

b) `Lgt1` then the series is divergent.

c) `L=1` or does not exist  then the test is inconclusive. The series may be divergent, conditionally convergent, or absolutely convergent.

We may apply the Ratio Test to determine the convergence or divergence of the series `sum_(n=1)^oo (-1)^n/e^n` .

For the given series `sum_(n=1)^oo (-1)^n/e^n` , we have `a_n =(-1)^n/e^n` .

 Then,` a_(n+1) =(-1)^(n+1)/e^(n+1)` .

We set up the limit as:

`lim_(n-gtoo) | [(-1)^(n+1)/e^(n+1)]/[(-1)^n/e^n]|`

 To simplify the function, we flip the bottom and proceed to multiplication:

`| [(-1)^(n+1)/e^(n+1)]/[(-1)^n/e^n]| =| (-1)^(n+1)/e^(n+1)*e^n/(-1)^n|`

Apply Law of Exponent: `x^(n+m) = x^n*x^m` . It becomes:

`| ((-1)^n (-1)^1)/(e^n *e^1)*e^n/(-1)^n|`

Cancel out common factors `(-1)^n and`` e^n` .

`| (-1)^1/ e^1 |`

Simplify:

`| (-1)^1/ e^1 | =| (-1)/ e |`

          ` = |-1/e| `

          ` =1/e`

Applying `| [(-1)^(n+1)/e^(n+1)]/[(-1)^n/e^n]|= 1/e` , we get:

`lim_(n-gtoo) | [(-1)^(n+1)/e^(n+1)]/[(-1)^n/e^n]|=lim_(n-gtoo) 1/e`

`lim_(n-gtoo) 1/e=1/e or 0.3679` (approximated value)

 The limit value  `L~~0.3679` satisfies the condition: `L lt1` .

 Therefore, the series `sum_(n=1)^oo (-1)^n/e^n` is absolutely convergent.

What are two things that cause us to doubt ourselves, according to Emerson?

Two things that cause us to doubt ourselves are not being true to the inner voice of our souls and failing in our first endeavor.

Emerson contends that we doubt the divine spark that God has placed within us if we constantly look to the past or the future for inspiration. He advises young men to throw away their books and live in the present moment. He points to plants, saying they are not looking...

Two things that cause us to doubt ourselves are not being true to the inner voice of our souls and failing in our first endeavor.

Emerson contends that we doubt the divine spark that God has placed within us if we constantly look to the past or the future for inspiration. He advises young men to throw away their books and live in the present moment. He points to plants, saying they are not looking to the past but being true to themselves as they grow and blossom. He writes the following:

Thus all concentrates: let us not rove; let us sit at home with the cause. Let us stun and astonish the intruding rabble of men and books and institutions.

Likewise, while we need to care for our family and friends, we cannot allow them or their ideas of what we ought to do shake us from our true path: 

Say to them, O father, O mother, O wife, O brother, O friend, I have lived with you after appearances hitherto. Henceforward I am the truth’s.

Emerson also writes that,

If our young men miscarry in their first enterprises, they lose all heart.

Instead, he says, we should brush off failure, hop up, and try again. The world is a big place and full of opportunities. If we have not found our destined path on the first try, there are a hundred more paths to explore. The key is to keep trying and to have faith that we will eventually succeed.

How does A Theory of Justice by John Rawls relate to urban planning?

Rawls does not specifically discuss urban planning in the book, which is more theoretical and philosophical than most books about such a pragmatic topic as urban planning. Essentially, Rawls argues in the book that if we were able to choose the kind of society we lived in, we should do it from behind a veil of ignorance, meaning that we don't know what our own abilities, or position in society will be. Without knowing where...

Rawls does not specifically discuss urban planning in the book, which is more theoretical and philosophical than most books about such a pragmatic topic as urban planning. Essentially, Rawls argues in the book that if we were able to choose the kind of society we lived in, we should do it from behind a veil of ignorance, meaning that we don't know what our own abilities, or position in society will be. Without knowing where we would fall in society, we would probably choose a society with the kind of social safety nets that protect everyone's basic welfare. Because urban planning is fraught with social issues, we could suggest the same thing about it. All sorts of issues related to urban planning have social implications. Gentrification, equal access to utilities, schools, public parks, and de facto segregation are all issues that involve the kind of fundamental justice that Rawls advocates for society as a whole. If we could choose the ideal city, all things being equal, we would choose a city where we had access to the same things as everyone else. In many ways, concrete issues like city planning are arenas where Rawls's ideas of justice might be (but all too often are not) put into practice.

How did the U.S. strategize the winning of the Vietnam War using "organized modern technology"?

Historian Howard Zinn is credited with saying, “When the United States fought in Vietnam, it was organized modern technology versus organized human beings, and the human beings won.”

After the signing of the Geneva Agreement in 1954, French forces withdrew from what was then French Indochina. The agreement led to the recognition of communist North Vietnam and formed the new country of South Vietnam. Despite a hegemonic party holding power in the south, the United States supported the non-communist government. Initially US support was focused on economic and strategic aid, not military assistance. Over time there was a mission creep, and US military trainers became combat advisors. Increased pressure from the communist North Vietnamese Army (NVA) and the southern National Liberation Front, or Viet Cong (VC), led to more US military involvement. In 1964 there were approximately 23,000 US troops in Vietnam; just one year later the number was 184,000. With the huge influx of American combat troops came American doctrine.

Facing a dispersed rebellion (VC) and a conventional military front (NVA), U.S. forces had to rely on mobility, firepower, and air superiority. Both the NVA and VC armies were peasant forces, supplied and equipped with Soviet Block weapons, mostly funneled through other communist countries, like China. With a huge local recruiting pool, the communist forces seemed to have an inexhaustible supply of willing recruits. The best “method” to counter numerical superiority was believed to be the application of “organized modern technology.”

The US launched a strategic air campaign reminiscent of the great World War II bombing campaigns. The US established interlocking fire-bases on hilltops; developed a vast network of support bases, forward operating bases, and combat outposts; and assembled an enormous air presence to root out the VC. Utilizing light, small scout helicopters, US commanders sought out hostile troops, initiated contact, and launched large-scale infantry assaults, most commonly using troop-carrying helicopters to identify and eliminate the enemy.

With dynamic battlefield communications, intelligence-gathering, and interlocking support, troops worked together. Infantry troops relied on local artillery pieces, assault helicopters, jet bombers, and, in some cases, naval gunfire support. By utilizing a wide range of combined arms, the technological advantage leveled the battlefield. Multiple captured NVA and VC leaders reported a similar tactical doctrine: “We had to close with the Americans, we always fixed bayonets. By getting close we were able to limit the effectiveness of American artillery and air support.”

Despite a strategic loss, US troops were seldom defeated in force-on-force battles at the tactical level. Instead, the VC and NVA practiced hit and run, guerrilla, ambush, and tunneling tactics to inflict casualties and win a war of attrition. In many ways, the American failure to sustain South Vietnam as a democratic country is analogous to the American victory against the British nearly two hundred years earlier.

Who makes the decisions in a democracy?

In the traditional meaning of democracy, all members of a group contribute to the decision making process, typically through voting. In fact, the term "democracy" comes from the Greek demokratia, meaning "people's rule." In reality, there have been very few true democracies due to the difficulties of implementing this form of government on such a large scale.

In Ancient Greece, where democracy originated, the only real acting members of a democracy were adult males of wealth....

In the traditional meaning of democracy, all members of a group contribute to the decision making process, typically through voting. In fact, the term "democracy" comes from the Greek demokratia, meaning "people's rule." In reality, there have been very few true democracies due to the difficulties of implementing this form of government on such a large scale.

In Ancient Greece, where democracy originated, the only real acting members of a democracy were adult males of wealth. Children, for obvious reasons, were not allowed to vote, but neither were women or slaves. In more modern times, democracies exist based on the agreement that all persons, regardless of gender, class, bodily ability, or ethnicity, are given the right to vote. In the United States, this is the understanding, but it's much more complicated in implementation! Imagine if a group of one hundred people broke up into groups of ten and each elected an individual to vote in a committee of the ten representatives.  This is similar to the representative democracy of the United States, where the masses vote for people who will represent them and vote on their behalf. 

Illustrate the differences between Henry and Victor's reactions on this trip in Chapter 19

Victor looks upon the trip, not as a nice vacation, but as more of a fact-finding mission. He wants to familiarise himself with the latest scientific developments in order to help him build the second monster. Victor, then, has a lot on his mind and so cannot enjoy the journey. In fact, it's a horrible experience for him as he's sunk deep in a dark depression. He's still emotionally torn between completing the second monster...

Victor looks upon the trip, not as a nice vacation, but as more of a fact-finding mission. He wants to familiarise himself with the latest scientific developments in order to help him build the second monster. Victor, then, has a lot on his mind and so cannot enjoy the journey. In fact, it's a horrible experience for him as he's sunk deep in a dark depression. He's still emotionally torn between completing the second monster or destroying it altogether. And he remembers all too well the sinister threat made against him by the monster if he didn't build him a mate. Victor just wants to get the journey over with as soon as possible and get on with his work.

Henry, on the other hand, enjoys the trip immensely. But then again, he isn't burdened by a seemingly unsolvable moral dilemma. He sees the trip as a great opportunity to engage in learned conversation with men of genius and talent. Victor admits that he would've felt the same way as Henry in his happier days. Henry is, as Victor himself acknowledges, Frankenstein's former self, the eager, inquisitive young scientist bursting with curiosity about the world around him.

Why goes Golding decide to introduce the parachutist in chapter 6?

In chapter 5, Ralph holds an assembly to discuss why the boys are neglecting their responsibilities and address their fear of the beast. Essentially, the boys' attempt at creating a civil society is failing, and they are gradually descending into savagery. Towards the end of the meeting, Jack openly defies Ralph and leaves the assembly unexcused. After the hunters follow Jack, Ralph and Piggy lament about their terrible situation and ask for a sign from...

In chapter 5, Ralph holds an assembly to discuss why the boys are neglecting their responsibilities and address their fear of the beast. Essentially, the boys' attempt at creating a civil society is failing, and they are gradually descending into savagery. Towards the end of the meeting, Jack openly defies Ralph and leaves the assembly unexcused. After the hunters follow Jack, Ralph and Piggy lament about their terrible situation and ask for a sign from the adult world.

At the beginning of chapter 6, a paratrooper is shot out of the sky and lands on the top of the mountain. The dead paratrooper's arrival is both ironic and significant. The dead paratrooper's ominous arrival symbolizes the presence of evil on the island and indicates that the boys' situation will only get worse. Golding strategically chose to introduce the dead paratrooper in chapter 6 because it is a turning point in the novel when the boys' circumstances become dramatically worse. Once the paratrooper lands on the island, the boys becoming increasingly savage and end up brutally murdering Simon three chapters later.