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what is the summation of \(\sum_{n=1}^\infty \log\left(\dfrac{n(n+2)}{(n+1)^2}\right) \)?

 

what is the summation of \(\displaystyle\sum_{n=1}^{\infty} (\sqrt[n]{2} - 1) \)?

what is the summation of \(\displaystyle\sum_{n=1}^{\infty}\dfrac{1}{n^{(n+1)/n}} \)?

 

 If there is no explicit answer just say it converges.

 Mar 29, 2021
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1) The sum is -1/2.

 

2) The sum is 4*sqrt(2).

 

3) The sum is e^2.

 Mar 30, 2021

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