Hey, I'm going over series expansions and was wondering if someone could check my work and tell me if my work is correct. If not, could you explain it to me? I couldn't find any example like this problem in my book so I'm posting it online. Here it is,(adsbygoogle = window.adsbygoogle || []).push({});

The closed form series expansion for cos(x) is Ʃ[(-1)^n(x)^2n]/(2n)!. Use this series to find a series expression for [cos(x)-1]/x^2.

Okay here's what I did:

[cos(x)-cos(pi)]/(x)^(2)

(x)^(-2)*Ʃ[(-1)^(n)(x)^(2n)-(pi)^(2n)]/(2n)!

Ʃ[(-1)^(n)(x)^(2n-2)-(pi)^(2n)

Is that the way I'm supposed to do it? Thanks!

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# Series expression

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