Question $9,10\mathrm{.}3\mathrm{.}60$

Part $1$ of $2$

HW Score:

$90\%,9$ of $10$

points

Points: $0$ of

$1$

For the following telescoping series, find a formula for the $n$th term of the sequence of partial sums $\{S_n\}.$ Then evaluate $\underset{?}{lim}{S}_n$ to obtain the value of the series or state that the series diverges.

${\displaystyle \underset{k=0}{\overset{}{}}}\frac{1}{(2k7)(2k9)}$

A formula for the $n$th term of the sequence of partial sums is $S_n=$

$$

$\sqrt[5]{13}$

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