Need help with a proof

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I need help with proving these 2 equations.
Just to check. You are defining
[imath]\displaystyle F_a(t) = \sum_{n = 0}^{\infty} a_n t^n[/imath]

and
[imath]\displaystyle F_b(t) = \sum_{m = 0}^{\infty} b_m t^m[/imath]

and you are trying to show that
[imath]\displaystyle F_a(t) F_b(t) = \sum_{n = 0}^{\infty} \sum_{m = 0}^{\infty} a_n b_m t^{n + m} = \sum_{k = 0}^{\infty} C_k t^k = F_C(t)[/imath]

Is that correct?

-Dan
 
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