For the following telescoping series, find a formula for the nth term of the sequence of partial sums
{S_(n)}
. Then evaluate
\lim_(n->\infty )S_(n)
to obtain the value of the series or state that the series diverges.
\sum_(k=1)^(\infty ) ((5)/(k)-(5)/(k+1))

Question

For the following telescoping series, find a formula for the nth term of the sequence of partial sums

{S_(n)}

. Then evaluate

\lim_(n->\infty )S_(n)

to obtain the value of the series or state that the series diverges.

\sum_(k=1)^(\infty ) ((5)/(k)-(5)/(k+1))

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