Sequences and series: sum[n=0,infty] 2^n/(a^(2^n)+1), a>1

Ishan

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Please help no clue from where to start

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\(\displaystyle \displaystyle{\sum_{n=0}^{\infty}\dfrac{2^n}{a^{2^n}+1}}\) where a>1

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Please help no clue from where to start

View attachment 7375

\(\displaystyle \displaystyle{\sum_{n=0}^{\infty}\dfrac{2^n}{a^{2^n}+1}}\) where a>1

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Let

2^n = u

Then the problem transforms to:

\(\displaystyle \displaystyle{\sum_{u=1}^{\infty}\dfrac{u}{a^{u}+1}}\) where a>1

continue....
 
Let

2^n = u

Then the problem transforms to:

\(\displaystyle \displaystyle{\sum_{u=1}^{\infty}\dfrac{u}{a^{u}+1}}\) where a>1

continue....
Sorry but after this I don't know what to do plz help

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Sorry but after this I don't know what to do plz help

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Tell us whether the series converges or diverges?

How is it that you are given problems that you cannot "start" and cannot continue after given hint/s?
 
Tell us whether the series converges or diverges?

How is it that you are given problems that you cannot "start" and cannot continue after given hint/s?
I don't know convergence or divergence I am in 11th class.

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I don't know convergence or divergence I am in 11th class.

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You never asked a question. Exactly what do you want to know? Do you just want to know the sum? So what have you learned about solving these types of problems. Have you tried finding the sum of the first few terms to see if it is approaching (getting close to) a certain number?
 
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You never asked a question. Exactly what do you want to know? Do you just want to know the sum? So what have you learned about solving these types of problems. Have you tried finding the sum of the first few terms to see if it is approaching (getting close to) a certain number?
I want to know how do I algebraically calculate the sum.
Using basics such as splitting numerator in simplified form ECT.

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If everything I can ask from my teacher then why is this forum created ?
Asking that question shows that you understand nothing about the purpose of this forum. We try to help people who know something about the subject but have a problem with a particular question. In your case, it appears that you have no basic material with which to work. We are not here to teach you anything. You are expected to already have a basic understanding of the material so that we can help you work through the problem yourself.
 
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