I don't know how to get this Σ(n=0 to infinity)[(-1)^n/(3^n*(2n + 1))]=(pi/2*sqrt(3)),
by using arctan(x) =Σ(n=0 to infinity) (-1)^n*[ x^(2n+1)/(2*n+1)], for all |x| <= 1.
by using arctan(x) =Σ(n=0 to infinity) (-1)^n*[ x^(2n+1)/(2*n+1)], for all |x| <= 1.
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just let x = 1 / √3...and it is ( 2n + 1 ) , not (2*n+1)...and π / [ 2 √3 ]