A) \[{{\left( \frac{n}{n+1} \right)}^{2}}\]
B) \[{{\left( \frac{n}{n+1} \right)}^{3}}\]
C) \[\left( \frac{n}{n+1} \right)\]
D) \[\left( \frac{1}{n+1} \right)\]
Correct Answer: C
Solution :
\[{{T}_{n}}=\frac{\frac{n(n+1)}{2.\,2}}{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}+.....+{{n}^{3}}}=\frac{\frac{n(n+1)}{4}}{{{\left( \frac{n(n+1)}{2} \right)}^{2}}}\] \[=\frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}\] \ \[{{S}_{n}}=\sum\limits_{{}}^{{}}{\left( \frac{1}{n}-\frac{1}{n+1} \right)}\] \[=\left( 1-\frac{1}{2} \right)+\left( \frac{1}{2}-\frac{1}{3} \right)+\left( \frac{1}{3}-\frac{1}{4} \right)+.......+\left( \frac{1}{n}-\frac{1}{n+1} \right)\] \[=1-\frac{1}{n+1}=\frac{n}{n+1}\].You need to login to perform this action.
You will be redirected in
3 sec