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Find the values of x for which the series converges, then find the sum of the series...

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user6978788 | Student, Undergraduate | Honors

Posted March 27, 2013 at 6:07 PM via web

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Find the values of x for which the series converges, then find the sum of the series for those values of x.

`sum_(n=0)^oo(x-1)^n/5^n`

Tagged with converge, diverge, limit, math, series

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degeneratecircle | High School Teacher | (Level 2) Associate Educator

Posted March 27, 2013 at 7:47 PM (Answer #2)

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This is a geometric series `sum_(n=0)^oo r^n` , where `r=(x-1)/5.` As with any geometric series, this series converges if and only if `|(x-1)/5|<1.` Solving for `x` gives `-4<x<6.`

The series converges if and only if `-4<x<6.`

For these values of `x,` the first term is always `1,` and the ratio between terms is `r.` The sum is thus

`1/(1-r)=1/(1-(x-1)/5)=5/(6-x).`

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