Channel: singingbanana

Category: Education

Tags: divergentriemann series theoremmathematicslogmathsinfiniteconvergentsumconditionally convergentproblempuzzleseriesriemannmathnatural log

Description: Riemann Series Theorem may be used to show ln(2) = (1/2)*ln(2) A formula for natural log: ln(1+x) = x - x^2/2 + x^3/3 - x^4/4 + ... for |x| less than or equal to 1. So ln(2) = 1 - 1/2 + 1/3 - 1/4 + .... More on the natural logarithm: en.wikipedia.org/wiki/Natural_logarithm Conditionally convergent: en.wikipedia.org/wiki/Conditionally_convergent Riemann Series Theorem: en.wikipedia.org/wiki/Riemann_series_theorem