$I_{n} = \int_{0}^{1} x^{n}e^{x-1}dx$
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