- #1
pupeye11
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Homework Statement
Let A(x) = [tex]\sum_{k>=0}a_{k}x^k[/tex] and B(x) = [tex]\sum_{k>=0}b_{k}x^k[/tex] show that:
A(X)B(X) = [tex]\sum_{k>=0}(\sum_{i=0}a_{i}b_{k-i})x^k[/tex]
The second sum sign in the answer should be from i=0 to k.
The Attempt at a Solution
I factored out like terms and then multiplied them together and got
[tex]\sum_{k>=0}x^k(a_{k}b_{k})[/tex] then if i={0,1,2,...,k} we would get
[tex]\sum_{k>=0}x^k(\sum_{i=0}a_{i}b_{k-i})[/tex]
I am guessing this is wrong?