1. ## Series questions!

(3) / n sqrt(n)

not sure what test i should use for this problem!

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[( -1 )^n] * [3^(n-2)] / 2^n

i dont understand why i cannot use this root test for this problem...it seems to work out fine and i get the limit = 0 so since L < 1 then it should be convergent....but this is actually supposed to be divergent.

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10n+3 / n2^n

another one i'm not sure which test i should use

2. Originally Posted by lochnessmonster
(3) / n sqrt(n)

not sure what test i should use for this problem!

-----------------------------------------------------

[( -1 )^n] * [3^(n-2)] / 2^n

i dont understand why i cannot use this root test for this problem...it seems to work out fine and i get the limit = 0 so since L < 1 then it should be convergent....but this is actually supposed to be divergent.

----------------------------------------------------------

10n+3 / n2^n

another one i'm not sure which test i should use
I am having a hard time reading the first one my guess is that it is this

$\displaystyle \displaystyle \sum_{n=0}^{\infty}\frac{3}{n\sqrt{n}}=\sum_{n=0}^ {\infty}\frac{3}{n^{\frac{3}{2}}}$

This is a p-series with $\displaystyle p=\frac{3}{2}$

$\displaystyle \displaystyle \sum_{n=0}^{\infty}\frac{(-1)^n3^{n-2}}{2^n}=3^{-2}\sum_{n=0}^{\infty}\left( \frac{-3}{2} \right)^n$

This is a geometric series or use the basic test for divergence!

For the last one I think this is the series

$\displaystyle \displaystyle \sum_{n=0}^{\infty}\frac{10n+3}{n2^n}$

Use the limit comparison test with $\displaystyle \displaystle b_n=\frac{1}{2^n}$ this is a convergent geometric series

3. Originally Posted by lochnessmonster
(3) / n sqrt(n)

Use the integral test.

[( -1 )^n] * [3^(n-2)] / 2^n

i dont understand why i cannot use this root test for this problem...it seems to work out fine and i get the limit = 0 so since L < 1 then it should be convergent....but this is actually supposed to be divergent.

Check your limit (it is not $\displaystyle 0$) . The limit $\displaystyle \lim_{n\to +\infty}( -1 )^n 3^{n-2} / 2^n$ does not exist, so the series is divergent.

10n+3 / n2^n another one i'm not sure which test i should use

Use the ratio test.

Edited: Sorry, I didn`t see the previous post.