sum of 1/2+1/4+1/6+1/8... n terms
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1/2 + 1/4 + 1/8 + ... = (1/2)/(1 - 1/2) = 1 This is sum to infinity of a geometric progression, with a = 1/2, r = 1/2 S(infinity) = a/(1 - r)
this follows http://en.wikipedia.org/wiki/Harmoni...s_(mathematics)
Originally Posted by gohpihan 1/2 + 1/4 + 1/8 + ... = (1/2)/(1 - 1/2) = 1 This is sum to infinity of a geometric progression, with a = 1/2, r = 1/2 S(infinity) = a/(1 - r) this maybe true but is not what the OP asked.
Originally Posted by pickslides this follows http://en.wikipedia.org/wiki/Harmonic_series_(mathematics) i have got the solution graphically as 1.2 but how to do it with zeta function
As pickslides said, that is the same as , the "harmonic series". Since is defined as , and so but I do not know of any way to write the partial sums.
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