# Powere Series Expansion and its Utilization in Integration

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Problem:

Given the power series for the following function (1+x)^k

(a) Write the power series for (1+x)^(1/3)

(b) Use the power series from part (a) to find the power series for x^3

(c) Using this series approximate the following integral (1+x^3) ^(1/3) using the first three terms

https://brainmass.com/math/integrals/power-series-expansion-utilization-integration-26966

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The solution is attached below in two files. The files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format ...

#### Solution Summary

Sometimes integration of a power series can give a very good approximation to the real result. This solution demonstrates how to use this method.

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