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If S(n)=(3)/(1^(2)+2^(2))+(7)/(1^(2)+2^(...

If `S_(n)=(3)/(1^(2)+2^(2))+(7)/(1^(2)+2^(2)+3^(2))+. . . . . . .. . . . . .` upto n terms, then value of `Lim_(ntooo) S_(n)` is equal to

A

`(1)/(2)`

B

1

C

5

D

6

Text Solution

Verified by Experts

The correct Answer is:
A
`S_(n)=underset(r=1)overset(n)(sum)((2r+1)/(1^(2)+2^(2)+ . . . . . +r^(2)))=underset(r=1)overset(n)(sum)(6(2r+1))/(r(r+1)(2r+1))=6underset(r=1)overset(n)(sum)((1)/(r)-(1)/(r+1))=(6n)/(n+1)`
`:." "underset(ntooo)LimS_(n)=underset(ntooo)Lim(n(6))/(n(1+(1)/(n)))=6`
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