Question

Find the sum of the series

Answer 1

\[1-\ln2+\frac{ (\ln2)^3 }{ 2! }-\frac{ (\ln2)^3 }{ 3! }+...\]

Answer 2

I'm thinking it has to do with e^x as

\[e^x = \sum_{n=0}^{\infty} \frac{ x^n }{ n! }\]

Answer 3

Should there be an exponent of 2 in the third term there?

Answer 4

maybe because it alternates think of \(e^{-x}\)

Answer 5

Yeah it should be 2, sorry about that.

Answer 6

Yeah, you're on the right track @Astrophysics but just keep in mind where the negative signs fall and how to fix anything if it arises.

Answer 7

Ah nice hint sat, I think I got this.

\[e^{-\ln2} \implies (e^{\ln2})^{-1}\]

something like this right?

Answer 8

This gives me 1/2 then

Answer 9

Yeah that looks write to me.

Answer 10

Cool, thanks man :)!