Question 464432
This is true if and only if


*[tex \LARGE \frac{1}{2} - \frac{1}{8} + \frac{1}{24} - \frac{1}{64} + ... = \ln {\frac{3}{2}}],


because it will satisfy the logarithm identity *[tex \log(ab) = \log(a) + \log(b)]. However, the above series is equal to ln 3/2. If you know the Taylor series for ln x centered at 1


*[tex \LARGE \ln{x} = (x-1) - \frac{1}{2}(x-1)^2 + \frac{1}{3}(x-1)^3...]


We can replace x = 3/2 and get a true result. Hence the original equation is true.