Thread: Infinite series of an exponent question.

I'm trying to evaluate the infinite series of e^Nx from N=0. As this expands to:
1 + e^x + e^2x + ... e^Nx

Can I treat it as a geometric series, where r = e^x, collapsing it to

1/(1 - e^x)?

Originally Posted by DenJansen

I'm trying to evaluate the infinite series of e^Nx from N=0. As this expands to: 1 + e^x + e^2x + ... e^Nx

If , As an infinite series that series diverges.

Ah, I see. Thank you both!

Wait, I just noticed something. As this is an infinite series from N=0 to N->∞, wouldn't the equation above simply = ∞? Is there a way to solve this where N is not in the final equation?

Originally Posted by DenJansen

Wait, I just noticed something. As this is an infinite series from N=0 to N->∞, wouldn't the equation above simply = ∞? Is there a way to solve this where N is not in the final equation?

I do not understand that question.
You have two different ideas going on: .
If , that is , then the series does converge.
Its sum is .

As I said in reply #2, if the series diverges.

So the answer depends upon the value of .
Whereas, is simply an index for the sum.