Series test

[AlexSendler100%]

Hello I need to prove that the next series is converges. But doesn't converges at absolute value (absolutely)
Can someone give me a test to start with because I tried the libniz test with derevetive and that seems like an awful step

 

[stapel]

Hello I need to prove that the next series is converges. But doesn't converges at absolute value (absolutely)
Can someone give me a test to start with because I tried the libniz test with derevetive and that seems like an awful step

The (huge) attachment contains two series:

[imath]\qquad \textrm{A) } \displaystyle{ \sum_{k=1}^{\infty} \frac{\cos(k) - \sin(k)}{\sqrt{k^4 + 1\;}} }[/imath]

[imath]\qquad \textrm{B) } \displaystyle{ \sum_{n=1}^{\infty} (-1)^n\, \left(\frac{1 + \sin\left(\frac{1}{n}\right)}{n}\right) }[/imath]

To which series are you referring?

When you reply, please include a clear listing of your thoughts and efforts so far, along with the tests that are available to you, so that the helpers can see what's going on.

Thank you!

 

[AlexSendler100%]

To series B and again can you give some kind of advice from which test to start or even some note to begin with

 

[skeeter]

[imath]\bigg|\sin\left(\frac{1}{n}\right) \bigg| \le 1 \implies \dfrac{1+\sin\left(\frac{1}{n}\right)}{n} < \dfrac{2}{n}[/imath]

 

[AlexSendler100%]

Thanks a lot ?