Series

[sinos]

hello,
I need help with the following questions:



prove of disprove:


many thanks for you help!

 

[Deleted member 4993]

hello,
I need help with the following questions:

View attachment 12913

prove of disprove:
View attachment 12914

many thanks for you help!

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[sinos]

Please follow instructions regarding posting at this forum - enunciated at:

READ BEFORE POSTING

Welcome to FreeMathHelp.com! Please take the time to read the following before you make your first post. It will help you to get your math questions answered promptly and in the most helpful manner. A summary is available here, but please read the complete guidelines below at your earliest...

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Please share your work/thoughts - so that we know where to begin to help you.

Okay. thank you,
I see now that you can't post two question at once than please ignore the second question.
As to where I got stuck - I got stuck at the very begining.
I thought about using heine and thats it.
Any ideas?

 

[pka]

I need help with the following question:
prove of disprove:
View attachment 12914

Suppose that \(\displaystyle a_n=\frac{(-1)^n}{\sqrt{n}}\) Use the alternating series test to prove that \(\displaystyle \sum\limits_{n = 1}^\infty {{a_n}} \) converges.
Now does the series \(\displaystyle \sum\limits_{n = 1}^\infty {{{\left( {{a_n}} \right)}^2}} \) converge?