# Proof involving integral

lordy2010

## Homework Statement

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

Show that 0 < $$I_{n}$$ < $$\frac{1}{n+1}$$

n/a

## The Attempt at a Solution

I have been trying to prove this for a long time, and so far I haven't gotten anywhere. I managed to get a reduction formula for it using integration by parts, and I can prove that it is greater than 0, but not that it is less than 1/(n+1). I have tried using induction too, but with no luck.