If x = 1 + a + a^2 + a^3 + ... y = 1 + b + b^2 + b^3 + ... then show that 1 + ab + a^2b^2 + a^3b^3 + ... = xy/(x + y - 1). How to go about this. Guidance required. Thanks. Aranga
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Originally Posted by arangu1508 If x = 1 + a + a^2 + a^3 + ... y = 1 + b + b^2 + b^3 + ... then show that 1 + ab + a^2b^2 + a^3b^3 + ... = xy/(x + y - 1). How to go about this. Guidance required. Thanks. Aranga I'm going to assume that and . Then
We are given: Multiply through by : Likewise, we find: Now, use a similar method, where: Then, after multiplying through by solve for , then use your values of and to get the desired result.
Hello, arangu1508! Another approach . . . From [1]: . From [2]: . We have: .
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