Question

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

Answer 1

Answer:

  $S_8=\dfrac{1640}{27}=60\frac{20}{27}$

Step-by-step explanation:

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

  $S_n=a_1\dfrac{1-r^n}{1-r}$

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

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