text: how can i find the sum of this series? a(n)=(1/(2n-1))*(1/(a^(2*n-1))... s(n)=a(1)+a(2)+...+a(n)=???? if i understand this right, you have a(n) = a^(-2n + 1)/(2n - 1), so  s(n) = 1/a + 1/(3a^3) + 1/(5a^5) + ...  let f(x) =x^(-2n + 1)/(2n - 1) = x^(-1) + x^(-3)/3 + x^(-5)/5 + ...  then f'(x) (derivative of x) is  f'(x) = -x^(-2) - x^(-4) - x^(-6) - ...  this is a power series and can be summed over the range it converges as -x^(-2)/(1 - x^-2), then you need to integrate to get the actual function.