Question

Given the series: \[ \sum_{k=1}^{\infty} \frac{1}{k(k+2)} \] does this series converge or diverge? diverges converges If the series converges, find the sum of the series: \[ \sum_{k=1}^{\infty} \frac{1}{k(k+2)}= \] $ \square $ (If the series diverges, just leave this second box blank.) Hint: Try breaking up the summand using partial fractions.

          Given the series:
\[
\sum_{k=1}^{\infty} \frac{1}{k(k+2)}
\]
does this series converge or diverge?
diverges
converges

If the series converges, find the sum of the series:
\[
\sum_{k=1}^{\infty} \frac{1}{k(k+2)}=
\]
\( \square \)
(If the series diverges, just leave this second box blank.)
Hint: Try breaking up the summand using partial fractions.

$Given the series: ∑k=1^∞(1)/(k(k+2)) does this series converge or diverge? diverges converges If the series converges, find the sum of the series: ∑k=1^∞(1)/(k(k+2))= □ (If the series diverges, just leave this second box blank.) Hint: Try breaking up the summand using partial fractions.$

Added by Jason M.

Question

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