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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

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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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