Originally Posted by

**zg12** I need to show that the limit of the sequence,

$\displaystyle \frac{{n + 1}}{{{n^2}}} + \frac{{{{(n + 1)}^2}}}{{{n^3}}} + \cdots + \frac{{{{(n + 1)}^n}}}{{{n^{n + 1}}}}$

is e-1. What's sad is I have the solution in front of me and I can't understand the simple algebra.

$\displaystyle \frac{{n + 1}}{{{n^2}}}\left[ {\frac{{1 - {{\left( {\frac{{n + 1}}{n}} \right)}^n}}}{{1 - \frac{{n + 1}}{n}}}} \right] = \frac{{n + 1}}{n}\left[ {{{\left( {1 + \frac{1}{n}} \right)}^n} - 1} \right]$

The second factor on the left, how did they get that?