Suppose we have two convergent geometric series ∑x^n and ∑y^n. Does it ever occur that ∑x^n∑y^n=∑[(x^n)(y^n)]? THANKS.
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Originally Posted by eg37se Suppose we have two convergent geometric series ∑x^n and ∑y^n. Does it ever occur that ∑x^n∑y^n=∑[(x^n)(y^n)]? Try . There is a general solution. Can you find it?
Originally Posted by eg37se Suppose we have two convergent geometric series ∑x^n and ∑y^n. Does it ever occur that ∑x^n∑y^n=∑[(x^n)(y^n)]? THANKS. I would say yes. Assume that the lead term is and that starts at then and so what you're asking is are there soltions to . I believe there are an infinite number of solutions to this equation on this interval.
Originally Posted by Plato Try . There is a general solution. Can you find it? Wouldn't it just be (1-(1/8)+(1/64)-(1/256)+...) which is just ∑(-1/8)^n?
Originally Posted by eg37se Wouldn't it just be (1-(1/8)+(1/64)-(1/256)+...) which is just ∑(-1/8)^n? If you substitute the x and y values that Plato suggests into the forumula I give Originally Posted by Danny . I believe that you'll show they're identical.
Got it. Thank you.
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