Find the sum of the series:
1/5 + 1/7 +1/5² +1/7² +...... to infinity.
Answers
Answer:
5/12
Step-by-step explanation:
1/5+1/7+1/5²+1/7²+..........
1/5 + 1/7 + 1/5² + 1/7² + 1/5² + 1/7³ +..........+ infinity ( here is a symbol of infinity. )
(1/5 + 1/5² + 1/5³ +.........infinity ) + (1/7 + 1/7² + 1/7³ +... infinity)
1/5²/1/5=5/5²=1/5 a2=1/7
a1 =1/5 r2=1/7
r1=1/5
sum of infinite G.P = a/1-r
a1/1-r1+a2/1-r2
1/5/1-1/5+1/7/1-1/7
1/5/4/5+1/7/6/7
= 1/4+1/6
= 3+2/12
= 5/12
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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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