Sum 1/5+1/7+1/5^2 +1/7^2........ to infinity
Answers
Given : 1/5 + 1/7 + 1/5² + 1/7² + .. + .. + .. + ∞
To Find : Sum
Solution:
1/5 + 1/7 + 1/5² + 1/7² + .. + .. + .. + ∞
Break this into 2 series
1/5 + 1/5² + 1/5³ + .. + .. + .. + ∞
1/7 + 1/7² + 1/7³ + .. + .. + .. + ∞
1/5 + 1/5² + 1/5³ + .. + .. + .. + ∞
a = 1/5
r = 1/5
S = a/(1 - r)
(1/5)/(1 - 1/5)
= (1/5)/(4/5)
= 1/4
1/7 + 1/7² + 1/7³ + .. + .. + .. + ∞
a = 1/7
r = 1/7
S = a/(1 - r)
(1/7)/(1 - 1/7)
= (1/7)/(6/7)
= 1/6
1/5 + 1/7 + 1/5² + 1/7² + .. + .. + .. + ∞ = 1/4 + 1/6
= (3 + 2)/12
= 5/12
1/5 + 1/7 + 1/5² + 1/7² + .. + .. + .. + ∞ = = 5/12
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