Proof of $\sum_{n=0}^{\infty }a_nt^n\sum_{k=0}^{\infty}b_kt^k=\sum_{n=0}^{\infty }(\sum_{k=0}^{\infty}a_{n-k}b_k)t^n$

Asked Nov 29 '20 at 12:10

Active Nov 29 '20 at 12:10

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How to prove this identity? $$\sum_{n=0}^{\infty }a_nt^n\sum_{k=0}^{\infty}b_kt^k=\sum_{n=0}^{\infty }(\sum_{k=0}^{\infty}a_{n-k}b_k)t^n$$ I found it on a textbook but there was no proof...

asked Nov 29 '20 at 12:10

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Can you prove it term wise? IE What is the coefficient of $ t^2$ on the LHS? and on the RHS? – Calvin Lin Nov 29 '20 at 12:15
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https://math.stackexchange.com/q/934835/42969 – Martin R Nov 29 '20 at 12:19

Proof of $\sum_{n=0}^{\infty }a_nt^n\sum_{k=0}^{\infty}b_kt^k=\sum_{n=0}^{\infty }(\sum_{k=0}^{\infty}a_{n-k}b_k)t^n$

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