document.write( "Question 419137: I hope someone can help me also with this question, \"The sum of an infinite geometric series is twice its first term. Find the common ratio of the series.\" This question has been eating at my brain for quite some time now. I hope you can help. Thank you. \n" ); document.write( "

Algebra.Com's Answer #293180 by ewatrrr(24785) $\"\"$ $\"About$

You can put this solution on YOUR website!


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document.write( "Hi
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document.write( "\"The sum of an infinite geometric series is twice its first term.
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document.write( " Find the common ratio of the series
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document.write( " =  when |r| < 1
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document.write( "a/(1-r) = 2a
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document.write( " 1/(1-r) = 2
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document.write( "   1 = 2 - 2r
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document.write( "   2r = 1
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document.write( "    r = 1/2\r
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document.write( "In general: the sum of a geometric series is:
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document.write( "  
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document.write( "As the 'infinite' sum being just twice it's first term, was safe, in my mind,
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document.write( "to assume that r was a fraction and r^n would become so...insignificant that (1-r^n)= 1  
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document.write( "For ex:  (1/2)^20 = .0000001 demonstrates that processs
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