Approximate the value of the series to within an error of at most $10^{-5}$. $sum_{n=1}^{infty} frac{(-1)^{n+1}}{n^6}$ Apply Theorem (3) from Section 10.4 to determine $|S - S_N| < b_{N+1}$ the smallest value of $N$ that approximates $S$ to within an error of at most $10^{-5}$. $N = $ $S approx $
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