SOLUTION: Given a geometric series with first term a > 0 and common ration r > 0 prove that a finite �sum to infinity� exists if and only if r < 1 and show that in this case the sum to infin

Question 549782: Given a geometric series with first term a > 0 and common ration r > 0 prove that a finite �sum to infinity� exists if and only if r < 1 and show that in this case the sum to infinity is .
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
We prove that a convergent sum exists by evaluating the limit as the number of terms approaches infinity:

Since r^(n+1) tends to zero, the sum converges to 1/(1-r). However, this only holds when |r| < 1. Otherwise, the limit diverges.
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