How do you find the sum of the infinite geometric series with $a_1=-5$ and $r=1/6$ ?

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How do you find the sum of the infinite geometric series with $a_1=-5$ and $r=1/6$ ?

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Answer 1 · 2014-07-23T21:42:07

A geometric series of first term $a$ and common ratio $r$ is divergent if $|r|>=1$ , and convergent if $|r|<1$ , in which case the sum is given by the formula $a/(1-r)$ . In the present case $r=1/6$ is less than 1 in absolute value, so that the series is convergent and its sum is $-5/(1-(1/6))=-6$ . See Geometric Series

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How do you find the sum of the infinite geometric series with $a_1=-5$ and $r=1/6$ ?

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How do you find the sum of the infinite geometric series with a_1=-5a_1=-5 and r=1/6r=1/6?

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How do you find the sum of the infinite geometric series with $a_1=-5$ and $r=1/6$ ?