Multiplying McLaurin Functions & Power Series

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jaejoon89
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How do you multiply McLaurin functions by "regular" power series?
For example:

If y' = sum (1, inf.) n*a_n x^n-1 and cos(x) = sum(0, inf.) (-1^n x^2n) / (2n)!, how do you find the product?

If y = sum(0, inf.) a_n x^n and sin(x) = sum(0, inf.) (-1^n x^(2n+1)) / (2n+1)!, how do you find the product of sin(x), y, and x?
 
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