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Homework Statement
Find the exact sum of:
[itex]\sum[/itex] 2/(n7n)
n=1->∞
The Attempt at a Solution
Let Sn denote the nth partial sum.
ln(Sn) = [itex]\Sigma[/itex] ln(2/(n7n))
=[itex]\Sigma[/itex] ln2 - lnn - nln7
= nln2 - (ln1 + ln7 + ln2 + 2ln7 + ln3 + 3ln7 ...)
= nln2 - ln(n!) - ln7[itex]\Sigma[/itex] n
= ln (2n)/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.