[Step-by-Step] Calculate the first ten terms of the series ∑limits_n=1^∞ (sin ^2n)/(n^3) and then estimate the error made in using this partial


Question: Calculate the first ten terms of the series

\[\sum\limits_{n=1}^{\infty }{\frac{{{\sin }^{2}}n}{{{n}^{3}}}}\]

and then estimate the error made in using this partial sum to approximate the sum of the series.

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