Find the taylor series for xex about x = 0. then integrate term-by-term and substitute to show that the series

Question

Theodore Valentine

Mathematics

23 January, 08:28

Find the taylor series for xex about x = 0. then integrate term-by-term and substitute to show that the series

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Brandon Mcintosh · Answer 1

The Taylor series for e^x about x = 0 is

1 + x + x^2/2! + x^3/3! + x^4 / 4! + ...

xe^x = x + x^2 + x^3/2! + x^4/3! + x^5/4! + ...

Integrating term by term gives:-

x^2 / 2 + x^3/3 + x^4 / 3.2! + x^5 / 4.3! + x^6 / 5.4! + ...