Question

Improper integral

Answer 1

Find the exact value of \[\int\limits_{1}^{\infty} \lfloor x \rfloor e^{-x} dx\]

Answer 2

floor function eh ...

Answer 3

yeah, i am out of idea for the floor function

Answer 4

maybe some kind of series? just a thought

Answer 5

\[1e^{-x}+2e^{-x}+3e^{-x}+...\]seems like it would find the area

Answer 6

i think that will do it

Answer 7

or integrate each blurb from a to b