It Can Be Shown That $\int _ { 0 } ^ { \infty } x e ^ { - x } d x$

question 19

True/False

It can be shown that $\int _ { 0 } ^ { \infty } x e ^ { - x } d x$ = 1. Use this fact and the integral test to construct an appropriate convergent infinite series. Is $\sum _ { \mathrm { k } = 0 } ^ { \infty } \mathrm { e } ^ { - \mathrm { k } }$ the correct series?