Sunday, February 7, 2016

calculus - Why $sum_{k=0}^infty (-1)^k frac{(ln 4)^k}{k!}=0.25$?



Hi can someone please explain why



$$\sum_{k=0}^{\infty} \frac{(-1)^k (\ln 4)^k}{k!} = 0.25$$



Your help is appreciated.


Answer



That expression is same as $e^{-ln(4)}$, and this is in fact $1/4$, i.e $0.25$



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