Grade 12Algebra
Compute the infinite sum V1 where V = 1/2 - 2/4 + 3/8 - 4/16 + 5/32 - 6/64 +… ∞?(a) 2/3(b) 2/9 ((c) 1/6(d) 2/27
Compute the infinite sum V1 where V = 1/2 - 2/4 + 3/8 - 4/16 + 5/32 - 6/64 +… ∞?
(a) 2/3
(b) 2/9 (
(c) 1/6
(d) 2/27
1 Answer
Aditya Gupta
consider the sum of infinite gp:
x – x^2 + x^3 – x^4 + ….= x/(1 + x)
now differentiate both sides
1 – 2x + 3x^2 – 4x^3 + ...= 1/(1+x)^2
multiply by x both sides
x – 2x^2 + 3x^3 – ….= x/(1+x)^2
now put x= ½
1/2 - 2/4 + 3/8 - 4/16 + 5/32 - 6/64 +… ∞ = 2/9
kindly approve :)
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