Question

Is the series convergent or divergent?

I don't know where to start.
I'll type it below.

Answer 1

You need to perform a convergence test on the given series.

Answer 2

You didn't write out the series, but I will say that there are many different convergence tests.

Answer 3

Here are a few:

Ratio test
Integral test
Comparison test
etc.

http://en.wikipedia.org/wiki/Convergence_tests

Answer 4

\[\sum_{n=1}^{\infty}e ^{n}/n ^{2}\]

Answer 5

Do divergent test, does it go to zero as n approach infinity?

Answer 6

This is a problem in the chapter before all of the tests you listed.

Answer 7

Well its fairly obvious that this series diverges.

Answer 8

as n approaches infinity, this ratio does not tend to zero, hence it is diverges

Answer 9

Since the exponential function grows much faster than n^2

Answer 10

is there another way to show this or I can only look at the graphs?

Answer 11

Divergence test is usually first test performed to see whether a series converges or diverges

Answer 12

in this case divergent test shows infinity/infinity, so I'm not so sure.

Answer 13

Use L'Hospitals rule or the taylor expansion of e^n to show divergence as n->infinity

Answer 14

Do L'Hopital you will see e^x grows much faster than x^2

Answer 15

thank you.

Answer 16

Ratio test:
\[\large L = \lim_{n\to \infty}\frac{\frac{e^{n+1}}{(n+1)^2}}{\frac{e^n}{n^2}} = e\]
L > 1
Series diverges