Question

An infinite geometric series has 1 and 1/5 as its frist two terms:1, 1/5' 1/25' 1/125' what is the sum,s,of the infinite series?

A 1/4
B1/25
c 5/4
d 1

Answer 1

you have a geometric series

since you are summing the powers of 1/5, this converges
(1/5 < 1)

it's equal to 1/(1-1/5)
=1/(4/5) = 5/4

for geometric series, the sum is always
x = 1/(1-r)
where r is the ratio of successive terms.

if you set the sum equal to x:
x = 1+r+r^2+r^3...
and multiply each term by r
rx= r+r^2+r^3+....
then subtract

x-rx = 1+r-r+r^2-r^2+r^3-r^3+....

x-rx = 1
x(1-r)=1
x=1/(1-r)