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Let S(n),n=1,2,3,"…" be the sum of infin...

Let `S_(n),n=1,2,3,"…"` be the sum of infinite geometric series, whose first term is n and the common ratio is `(1)/(n+1)`. Evaluate `lim_(n to oo)(S_(1)S_(n)+S_(2)S_(n-1)+S_(3)S_(n-2)+"..."+S_(n)S_(1))/(S_(1)^(2)+S_(2)^(2)+"......"+S_(n)^(2))`.

A

`(1)/(2)`

B

`(3)/(4)`

C

1

D

`- (1)/(2)`

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