Question

Find the sum of the series 81-27+9......-1/27.​

Answer 1

`S_8=(1640)/(27)=60(20)/(27)`

Explanation:

The formula for the sum of a geometric series with first term a1, common ratio r, and n terms is ...

`S_n=a_1(1-r^n)/(1-r)`

This series has 8 terms, a common ratio of -1/3, and a first term of 81. Its sum is ...

`S_8=81(1-(-(1)/(3))^8)/(1-(-(1)/(3)))=81(6560/6561)/(4/3)=(6560(3^4)(3))/((4)(3^8))\\\\\boxed{S_8=(1640)/(27)=60(20)/(27)}`