Question

DOES THIS SERIES CONVERGES OR DIVERGES, IF IT CONVERGES FIND THE LIMIT
------(e^x)/2^x

Answer 1

Is this the problem? $$\sum _{n=1}^\infty \frac{e^n}{2^n}$$Saying if this series converges or diverges?

Answer 2

Yes it is

Answer 3

Think of it like this: $$\sum _{n=1}^\infty \left(\frac{e}{2}\right)^n.$$ What type of series is this? How do we know when that type converges or diverges?

Answer 4

wont it diverge cause the higher the n goes to, the closer to infinity it get , right?

Answer 5

Yep. Its a geometric series, and \(\frac{e}{2}>1\), so yes, the terms will get bigger and bigger.