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

Question

asked Jul 27, 2021 204k views

1 Answer

Jay Edwards · Answer 1 · 2021-08-02T04:03:31+0000

Answer:

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 ...

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