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Partial sums & series

The nthn\text{th} partial sum of the series SS is given by
Sn=−2n(n+1)(n+2)\displaystyle{{S}_{n}}=-\frac{2n}{(n+1)(n+2)}.
S=S=
  • Your answer should be
  • an integer, like 66
  • an exact decimal, like 0.750.75
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4