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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 toA. `(1)/(2)`B. 1C. 5D. 6 |
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Answer» Correct Answer - 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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