Find the sum of the infinite series 1+(1+a)r+(1+a+a^2)r^2+(1+a+a^2+a^3)r^3............ .............
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Originally Posted by matsci0000 Find the sum of the infinite series 1+(1+a)r+(1+a+a^2)r^2+(1+a+a^2+a^3)r^3............ ............. Note that this is the same as . If and , then it follows that
Last edited by Chris L T521; Aug 23rd 2009 at 11:28 AM. Reason: fixed major mistake
Originally Posted by Chris L T521 If and , then it follows that How can you make this assertion though? Is this assumed somehow? The OP didn't include any restrictions on a or r.
Originally Posted by QM deFuturo How can you make this assertion though? Is this assumed somehow? The OP didn't include any restrictions on a or r. I imposed those conditions in order to evaluate the [geometric] series. Otherwise you can't [It diverges]!
Hello, matsci0000! Find the sum: . Multiply by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Therefore: .
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