document.write( "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 . \n" ); document.write( "

Algebra.Com's Answer #358222 by richard1234(7193) $\"\"$ $\"About$

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We prove that a convergent sum exists by evaluating the limit as the number of terms approaches infinity:\r
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\n" ); document.write( "\n" ); document.write( "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. \n" ); document.write( "

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