Question

I need someone to do this problem quickly as possible

Answer 1

The series for summation is,

`-(4)/(5),(16)/(26),-(64)/(125),\ldots`

The series is a geometric progression with a = -4/5 and r = -4/5.

The sum of infinite terms of a GP is,

`S_(\infty)=(a)/(1-r)`

Substitute the values in the sum formula to obtain the sum of infinite terms of a GP.

`\begin{gathered} S_(\infty)=(-(4)/(5))/(1-(-(4)/(5))) \\ =(-4)/(5\cdot(1+(4)/(5))) \\ =-(4)/(5)\cdot(5)/(9) \\ =-(4)/(9) \end{gathered}`

Answer: -4/9