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geometric progression

what do we get after multiplying two geometric progression series?
Original post by mandy sandhu
what do we get after multiplying two geometric progression series?


It depends how you multiply them.

Do you mean first term x first term, 2nd x 2nd etc?
Reply 2
If they are two general geometric progression series, then you will get a mess as each term has to be distributed out across the sum. Each term that is distributed across the sum will be itself a geometric progression.
(a+ar+ar^2+..ar^n.)(b+bk+bk^2+...bk^n)
a(b+bk+bk^2+...)+ar(b+bk+bk^2+...+bk^n)+ar^2+(b+bk+bk^2+...+bk^n)+...+ar^n((b+bk+bk^2+...+bk^n)
The first term in the sum will be itself a geometric series, first term ab and common ratio k, the second another geometric series, first term abr and common ratio again k, and so on.

So, I suppose the answer is that you will get a series of geometric series :smile: unfortunately not something simple, as the summation operator is linear: the rules exist for summing a variable times a constant and summing over a sum, but sadly there is no simple rule for when you multiply two sums together.

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