the sum of series :∑I/n2+2n fron n=1 to n=infinite is?????

Dear student,Thanks for your post. = = – = * ( - + – + – + …........)Now, all terms cancel out except 1 and ½, and since, n = infinity, last term tens to zero.* (+ ) =

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Algebra> the sum of series :∑I/n 2 +2n fron n=1 to...

the sum of series :∑I/n²+2n fron n=1 to n=infinite is?????

Mostafijur Rahaman , 10 Years ago

Grade 12

1 Answers

Shobhit Varshney

Last Activity: 10 Years ago

Dear student,

Thanks for your post.

$\sum$ $\frac{1}{n(n+2)}$ = $\sum$ $\frac{2}{n(n+2)}$ = $\frac{1}{2}$ $\sum$ $\frac{1}{n}$ – $\frac{1}{n+2}$

= $\frac{1}{2}$ * ( $\frac{1}{1}$ - $\frac{1}{3}$ + $\frac{1}{2}$ – $\frac{1}{4}$ + $\frac{1}{3}$ – $\frac{1}{5}$ + …........)

Now, all terms cancel out except 1 and ½, and since, n = infinity, last term tens to zero.

$\Rightarrow$ $\frac{1}{2}$ * ( $\frac{1}{1}$ + $\frac{1}{2}$ )

= $\frac{3}{4}$