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`lim_(nrarroo) [(1)/(n)+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+...+(1)/(8n)]` is equal toA. `(3)/(8)`B. `(1)/(4)`C. `(1)/(8)`D. None of these |
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Answer» Correct Answer - A `underset(nrarroo)(lim)[(1)/(n)+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+...+(1)/(8n)]` `" "=underset(nrarroo)(lim)[(n^(2))/((n+0)^(3))+(n^(2))/((n+2)^(3))+(n^(2))/((n+2)^(3))+...+(n^(2))/((n+n)^(3))]` `" "=underset(nrarroo)(lim)sum_(r=0)^(n)(n^(2))/((n+r)^(3))` `" "=underset(nrarroo)(lim)sum_(r=0)^(n)(1)/(n)(1)/((1+(r)/(n)))` `" "=int_(0)^(1)(dx)/((1+x^(3)))=[-(1)/(2(1+x)^(2))]_(0)^(1)` `" "=-(1)/(2)((1)/(4)-1)=(3)/(8)` |
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