A) n
B) \[\frac{1}{2}n\]
C) \[(n+1)\]
D) \[\frac{1}{2}(n+1)\]
Correct Answer: B
Solution :
| [b] \[\left( 1-\frac{1}{n+1} \right)+\left( 1-\frac{2}{n+1} \right)+\left( 1-\frac{3}{n+1} \right)+...+\left( 1-\frac{n}{n+1} \right)\] \[=\frac{n}{n+1}+\frac{n-1}{n+1}+\frac{n-2}{n+1}+...+\frac{1}{n+1}\] \[=\frac{n+(n-1)+(n-2)+...1}{(n+1)}\] \[=\frac{n\,(n+1)}{2}.\frac{1}{n+1}\] \[\left[ \therefore 1+2+3+...+n=\frac{n\,\,(n+1)}{2} \right]\] \[=\frac{n}{2}\] |
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