Remainders in alternating series Determine how
Chapter 10, Problem 33E(choose chapter or problem)
25-34. Remainders in alternating series Determine how many terms of the following convergent series must be summed to be sure that the remainder is less than \(10^{-4}\). Although you do not need it, the exact value of the series is given in each case.
\(\pi=\sum_{k=0}^{\infty} \frac{(-1)^{k}}{4^{k}}\left(\frac{2}{4 k+1}+\frac{2}{4 k+2}+\frac{1}{4 k+3}\right)\)
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