how do you solve a harmonic geometric progression like
S = 1/3(1/2)2 + 1/5(1/2)4 + 1/7(1/2)6 + ....∞
this question had options which were easy to eliminate but how do you solve this?
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3 Answers
62in these questions, you will have to go for special series..
like sin x
or cos x
or log x
there is no other method most of the times....
62−log(1 − x) = x + x^2/2+ x^3/3 + x^4/4+......................
−log(1 + x) = -x + x^2/2 - x^3/3 + x^4/4+......................
substract the two...
log(1 + x) −log(1 − x) = 2{ x + x^3/3 + x^5/5+......................)
x=1/2
log (3/2) - log(1/2) = 2(1/2 + 1/23/3 + 1/25/5....)
log(3) = (1 + 1/22/3 + 1/24/5....)
hence sum given is log 3-1