MCQ
${\sum\limits_{k = 1}^n {k\left( {1 + \frac{1}{n}} \right)} ^{k - 1}} = $
- A$n(n - 1)$
- B$n(n + 1)$
- ✓${n^2}$
- D${(n + 1)^2}$
$ = 1 + 2{\left( {1 + \frac{1}{n}} \right)^1} + 3{\left( {1 + \frac{1}{n}} \right)^2} + ....$upto n terms
$=1 + 2t + 3{t^2} + ...$ upto $n$ terms
$={(1 - t)^{ - 2}} = {\left[ {1 - \left( {1 + \frac{1}{n}} \right)} \right]^{ - 2}}$ = ${\left( {\frac{1}{n}} \right)^{ - 2}} = {(n)^2} = {n^2}$.
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