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

1 Answer
Nov 26, 2015

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