Question

What is the sum of the geometric series: 
3
∑5(-2/3)^i
i=0

Answer 1

We use the law of the sum of the 3 first terms of the geometric sequence:

`\sum_(i=0)^35\left((-2)/(3)\right)^i=5(1-\left((-2)/(3)\right)^4)/(1-\left((-2)/(3)\right))\\=5(\left((3^4-2^4)/(3^4)\right))/(\left((5)/(3)\right))\\=3\left((65)/(81)\right)=(65)/(27)`