- #1

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## Homework Statement

Find the exact sum of:

[itex]\sum[/itex] 2/(n7

^{n})

n=1->∞

## The Attempt at a Solution

Let S

_{n}denote the nth partial sum.

ln(S

_{n}) = [itex]\Sigma[/itex] ln(2/(n7

^{n}))

=[itex]\Sigma[/itex] ln2 - lnn - nln7

= nln2 - (ln1 + ln7 + ln2 + 2ln7 + ln3 + 3ln7 ...)

= nln2 - ln(n!) - ln7[itex]\Sigma[/itex] n

= ln (2

^{n})/n! - ln7 ([itex]\Sigma[/itex] n)

I'm not sure where to go from here, or if I'm even going in the right direction.