What is sum of the infinite geometric series for 1 -1/5 + 1/25 - 1/125 +

5/6

Step-by-step explanation:

Sum of infinite geometric series is given by formula a/(1-r).

where a is the first term

and r is the common ratio of geometric term.

Common ratio for a geometric series is given by  nth term/(n-1)th term.

Given series is

1 -1/5 + 1/25 - 1/125 +

step 1 : calculate r

for r lets use second and first term

2nd term = -1/5

1st term = 1

r = 2nd term/1st term = (-1/5) / 1 = -1/5

sum of this series = a/(1-r)

substituting a with 1 and r with -1/5, we have

sum of this series = 1/(1-(-1/5)) = 1/(1+1/5)

=> sum of this series =  1/((5+1)/5)

=> sum of this series =  1/ (6/5) = 5/6

sum of the infinite geometric series 1 -1/5 + 1/25 - 1/125 + is 5/6

2 x t divided by n

step-by-step explanation: