Question

Determine whether the series converges or diverges.

Answer 1

\[\sum_{n=1}^{\infty}\frac{ 1 }{ 2n-1 }\]

Answer 2

the values that are added on top get smaller and smaller
when they get close to infinity, they contribute almost nothing ( 0)

so I think the series converges to a value

Answer 3

how would i prove that? is this a p-series?

Answer 4

would i use the integral test?

Answer 5

Integral test would work

Answer 6

how would i set that up? im used to doing it with only one numberin the numerator.

Answer 7

denominator*

Answer 8

i got it! i got the answer to =1/

Answer 9

Basically, \[\sum_{n=1}^{\infty} \left(\frac{1}{2n - 1}\right)\] converges if and only if
\[\int_1^\infty \frac{1}{2x - 1} \mathrm{d}x\] is finite

Answer 10

The integral itself diverges (you can check this yourself probably), so the series diverge aswell

Answer 11

okay what about \[\frac{ 1 }{ n \sqrt{n^{2}-1} }\]

Answer 12

From n = 1?

Answer 13

yes

Answer 14

There's no sum if you start from n = 1, since when n = 1 you're dividing by zero

Answer 15

thts what i had so i just said it diverged becasuse the limit does not exist.