What is the sum of the infinity of series 1+7/10+(7/10)^2+(7/10)^3

1 answer

The series is a geometric series with first term 1 and common ratio 7/10. The sum of an infinite geometric series with first term a and common ratio r (where |r| < 1) is given by:

sum = a/(1-r)

Plugging in the values of a and r for our series, we get:

sum = 1/(1-7/10) = 1/(3/10) = 10/3

Therefore, the sum of the infinite series 1+7/10+(7/10)^2+(7/10)^3+... is 10/3.