. Let f(0) = 1 and f(n)(0) = (n + 1)!2n for n > 0.(a) Write the Taylor series for f at x
Chapter 10, Problem 40(choose chapter or problem)
. Let f(0) = 1 and f(n)(0) = (n + 1)!2n for n > 0.(a) Write the Taylor series for f at x = 0 using sigmasum notation. Simplify the general term. [Hint:Write out the first few terms of the Taylor series.](b) Does the series you found in part (a) converge forx = 3? Briefly explain your reasoning.(c) Use the series you found in part (a) to evaluate, 10f(x) dx. You may assume that, 10+n=1anxndx =+n=1, 10anxn dx.
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