Answer:
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.
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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
