A) 200
B) 199
C) 99
D) 19
Correct Answer: B
Solution :
\[{{T}_{n}}=\frac{\frac{n+(n+1)}{2}}{{{\left( \frac{n+(n+1)}{2} \right)}^{2}}}\] \[{{T}_{n}}=\frac{2}{n(n+1)}\] \[{{S}_{n}}=2\sum\limits_{n=1}^{n}{\left( \frac{1}{n}-\frac{1}{n+1} \right)}\] \[=2\,\left\{ \begin{matrix} 1-\frac{1}{2} \\ \frac{1}{2}-\frac{1}{3} \\ \end{matrix} \right.\]\[\left. \frac{1}{n}-\,\frac{1}{n+1} \right\}\] \[=2\left\{ 1-\frac{1}{n+1} \right\}\] \[\] \[100\times \frac{2n}{n+1}=n\] \[n+1=200\] \[n=199\]You need to login to perform this action.
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