1. ## Converge or diverge

hi everyone,

need help with this question

Test the alternating series for convergence or divergence.

$\displaystyle \sum ^\infty_{n=1} $$\displaystyle \frac {(-1)^{n-1}}{n^ \frac{1}{2}} can anyone help offer some guide, i'm stuck. thank you & regards,really appreciate all your help. 2. Originally Posted by anderson hi everyone, need help with this question Test the alternating series for convergence or divergence. \displaystyle \sum ^\infty_{n=1}$$\displaystyle \frac {(-1)^{n-1}}{n^ \frac{1}{2}}$

can anyone help offer some guide, i'm stuck.

thank you & regards,really appreciate all your help.
The alternating series has a well-known test for testing its convergence/divergence.
Do you know this test ?
Can you apply it on this problem ?

3. hi General

i know the test but i doint know how to apply for this question. please help clarify,really hope someone can help me out.

4. Originally Posted by anderson
hi General

i know the test but i doint know how to apply for this question. please help clarify,really hope someone can help me out.
For the series $\displaystyle \sum_{n=1}^{\infty} (-1)^{n-1} b_n$ , if:

1- $\displaystyle b_n > 0 \,\ \forall \,\ n \geq 1$

2- $\displaystyle b_n \geq b_{n+1}$ for all $\displaystyle n \geq 1$ , i.e. $\displaystyle b_n$ is decreasing.

3- $\displaystyle \lim_{n\to\infty} b_n = 0$.

Then the series converges.

Now, for your problem $\displaystyle b_n=\frac{1}{n^\frac{1}{2}}=\frac{1}{\sqrt{n}}$.

Can you apply the test on it?

5. Hi General

thank you so much for explaining,really appreciate