How Do You Solve the Series Sum n/2^(n-1)?

[djuiceholder]

Homework Statement

so I have learned how to do different problems of series.
but there's this problem that I spent hours last night but could not come up with anything.
which is-

∞
∑ n/2^(n-1)
n=1

Homework Equations

I have no idea

The Attempt at a Solution

so from there i was able to take out 2 and end up with: 2 n /(2^n)

i don't know how to do after that. however, i thought about doing (1/2)^n but then again it does not make sense to me.

help needed. i will appreciate that. thanks

 

[Mark44]

Why have you cross-posted this problem to this forum and the Precalc forum?

 

[Enjoicube]

Something tells me that the ratio test could helo here.

 

[Dick]

If you want to show the series converges, the ratio test can help. If you want to find the sum, the ratio test can't help. Hint: this looks like it's related to the series 1+x+x^2+x^3+... Take a derivative. Now figure out what to put x equal to.

 

[djuiceholder]

i was supposed to evaluate it. I don't know how though

 

[djuiceholder]

i posted this problem on a different folder and i was warned because it was a wrong place to post. anyways, i think i took it off