(1/2) * sum[n in A][(log(2))^n / n!]: How to find if this converges?

[mathjunior]

\(\displaystyle \displaystyle \dfrac{1}{2}\, \sum_{n \in A}\, \dfrac{(\log(2))^n}{n!}\)

\(\displaystyle A\, =\, \left\{0,\, 2,\, 4,\, ...,\, \infty\right\}\)

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How do i solve this? the n's in the A set are all even, i need to know what this series converges to and how to calculate it, i would appreciate your help, thank you!

 

[mathjunior]

how do i know what this series converges to? !



I need to know what this series converges to and how to calculate it, im in blank, i'm not really sure what todo, i've found a formula to solve this but it works if n goes from 0 to infinite without jumps, but this is not the case :/ Thank you!

 

[Deleted member 4993]

\(\displaystyle \displaystyle \dfrac{1}{2}\, \sum_{n \in A}\, \dfrac{(\log(2))^n}{n!}\)

\(\displaystyle A\, =\, \left\{0,\, 2,\, 4,\, ...,\, \infty\right\}\)

---

How do i solve this? the n's in the A set are all even, i need to know what this series converges to and how to calculate it, i would appreciate your help, thank you!

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