is Series converging, and need the sum

The series that has to be worked with in the problem is: `sum_(n=1)^oo (-1/8^n)`

`sum_(n=1)^oo (-1/8^n)`

= `-1/8 - 1/8^2 - 1/8^3 -...-1/8^oo`

It can be seen that as n becomes larger, `8^n` also becomes larger and its reciprocal `1/8^n` becomes smaller. At `n = oo` , `1/8^n = 0` .

The series `sum_(n=1)^oo (-1/8^n)` is an geometric series with with first term `a = -1/8` and common ratio `1/8` .

The sum of infinite terms of this series can be determined as the common ratio is less than 1.

The sum is `(-1/8)/(1 - 1/8)` = `-1/7`

The required sum of the series is -1/7

Comments

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