MATHS iQ CHALLENGE - #3(sUm To InFiNiTy)

Calculus Level pending

The sum to infinity of -

( Please provide the solution and reason)

none of these 1/16 1/24 5/48 1/5

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Abhisek Mohanty by Abhisek Mohanty , 21, India

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1 solution

Caleb Townsend
Mar 14, 2015

Let S S represent the sum. Also define A = 1 7 + 1 7 2 + 1 7 3 + . . . B = 1 7 2 + 1 7 4 + 1 7 6 + . . . S = A + B A = \frac{1}{7} + \frac{1}{7^2} + \frac{1}{7^3} + ... \\ B = \frac{1}{7^2} + \frac{1}{7^4} + \frac{1}{7^6} + ... \\ S = A + B
A = 1 7 + A 7 7 A = 1 + A A = 1 6 A\ =\ \frac{1}{7} + \frac{A}{7} \\ 7A\ =\ 1 + A \\ A\ =\ \frac{1}{6} B = 1 49 + B 49 49 B = 1 + B B = 1 48 B\ =\ \frac{1}{49} + \frac{B}{49} \\ 49 B\ =\ 1 + B \\ B\ =\ \frac{1}{48}
S = 1 6 + 1 48 = 3 16 S = \frac{1}{6} + \frac{1}{48} = \boxed{\frac{3}{16}}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Thanx man you did it so flawlessly . Really amazing solution , you cleared all my confusion

Abhisek Mohanty - 6 years, 3 months ago

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