Question-208322

Question Number 208322 by alcohol last updated on 11/Jun/24

Answered by Berbere last updated on 11/Jun/24

\underset{k = 1}{\prod^{n - 1}} {(1 + \frac{1}{k})}^{k} = \underset{k = 1}{\prod^{n - 1}} \frac{{(1 + k)}^{k}}{k^{k}} = \underset{k = 1}{\prod^{n - 1}} \frac{{(1 + k)}^{k + 1}}{(k + 1) . k^{k}}

= \underset{k = 1}{\prod^{n - 1}} \frac{1}{(k + 1)} . \underset{k = 1}{\prod^{n - 1}} \frac{{(1 + k)}^{k + 1}}{k^{k}} = \frac{1}{n!} . n^{n} = \frac{n^{n - 1}}{(n - 1)!}

Answered by MathematicalUser2357 last updated on 13/Jun/24

✓