Math

Alpha writes the infinite arithmetic sequence 10, 8, 6, 4, 2, 0...

Beta writes the infinite geometric sequence 9, 6, 4, 8/3, 16/9,...

Gamma makes a sequence whose n^th term is the product of the n^th term of Alpha's sequence and the n^th term of Beta's sequence: 10*9,8*6,6*4,4*8/3,2*16/9,...

What is the sum of Gamma's entire sequence?

I know this is a really long question but I need help.

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  1. Starting with n=0,
    An = 10-2n
    Bn = 9*(2/3)^n
    Gn = 18(5-n)*(2/3)^n

    By the ratio test, the series converges.
    Sum = 162

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  2. I really don't know the answer?

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