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Taylor Polynomials and Partial Sums of Series

1 Write the Taylor polynomial with center zero and degree 4 for the function f(x) = e^-x

2 Determine the values of p for which the series

∞
Σ 1/(2p)ⁿ
n=1

3 Calculate the sum of the first ten terms of the series, then estimate the error made using this partial sum to approximate the sum of the series

∞
Σ sinĀ²n/n^3
n=1

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