Shifting index of summation of power series

Thread starter dak246
Start date Mar 21, 2006
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Index Power Power series Series Summation

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SUMMARY

The discussion focuses on the manipulation of power series to align indices for solving equations. A participant suggests redefining the index of summation by letting j equal n-2, which transforms the first sum's power of x to x^j. To maintain consistency, they recommend redefining the second sum's index by letting j equal n, ensuring both sums utilize the same variable, x^j. This approach facilitates easier comparison and solution of the equation.

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Basic knowledge of algebraic transformations
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Mar 21, 2006

dak246

I can't seem to get these power series to match up so that I can solve the equation...heres my work:

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Mar 21, 2006

HallsofIvy

Science Advisor

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Looks to me like you went the "wrong direction".

Since the power of x in the first sum is n-2, let j= n-2 so the power becomes x^j. If having j in one sum and n in the other bothers you, let j= n in the second sum so it also has x^j.