$I_{n} = \int_{0}^{1} x^{n}e^{x-1}dx$
Show:
$0 < I_{n} < \frac{1}{n+1}$
The lower bound is obvious but my attempts to get an upper bound have been unsuccessful.
$I_{n} = \int_{0}^{1} x^{n}e^{x-1}dx$
Show:
$0 < I_{n} < \frac{1}{n+1}$
The lower bound is obvious but my attempts to get an upper bound have been unsuccessful.
When $0 < x <1$ note that $x^{n}e^{x-1} < x^{n}$ and if $f < g$ then $\int f < \int g$