Shifting index of summation of power series

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The discussion focuses on the challenges of aligning power series to solve an equation. One participant suggests that the original approach may have been incorrect and proposes a change in the index of summation. By letting j equal n-2, the power of x can be expressed as x^j. To maintain consistency, they recommend redefining j in the second sum to also equal n. This adjustment aims to simplify the problem and facilitate a solution.
dak246
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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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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 xj. If having j in one sum and n in the other bothers you, let j= n in the second sum so it also has xj.
 

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