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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- November 18th 2012, 11:18 PMarangu1508help in series
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 - November 18th 2012, 11:31 PMProve ItRe: help in series
- November 18th 2012, 11:45 PMMarkFLRe: help in series
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. - November 19th 2012, 07:40 AMSorobanRe: help in series
Hello, arangu1508!

Another approach . . .

Quote:

From [1]: .

From [2]: .

We have: .