1/2(1/2+1/3)-1/4((1)/(2^(2))+(1)/(3^(2))...

`1/2(1/2+1/3)-1/4((1)/(2^(2))+(1)/(3^(2)))+1/6((1)/(2^(3))+(1)/(3^(3)))+…infty` is equal to

A

`log_(e)2`

B

`log_(e)3`

C

`log_(e)sqrt(2)`

D

`log_(e)sqrt(3)`

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AI Generated Solution

To solve the given series \[ S = \frac{1}{2}\left(\frac{1}{2} + \frac{1}{3}\right) - \frac{1}{4}\left(\frac{1}{2^2} + \frac{1}{3^2}\right) + \frac{1}{6}\left(\frac{1}{2^3} + \frac{1}{3^3}\right) + \ldots \] we can break it down step by step. ...

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