Question

How do you find the sum of the infinite geometric series 2+2/5+2/25+2/125+...?

Answer 1

`sum_(i=0)^(oo) 2*(1/5)^i = 2.5`

Explanation:

General formula for an infinite geometric series sum `a+(a*r)+(a*r^2)+(a*r^3)+...` with `abs(r) < 1` is
`color(white)("XXX") a/(1-r)`

For the given series `a=2` and `r=1/5`
So the sum is
`color(white)("XXX")2/(1-1/5) = 2/((4/5)) = (2*5)/4 = 2 1/2`