Tuesday, February 28, 2017

Find the sum of the infinite series frac11cdot2+frac1cdot31cdot2cdot3cdot4+frac1cdot3cdot51cdot2cdot3cdot4cdot5cdot6+...


Find the sum of the series 112+131234+135123456+.... This type of questions generally require a trick or something and i am not able to figure that out. My guess is that it has something to do with exponential series or binomial series. Any help?



Answer



Sorry guys, got it.
112+131234+135123456+...=1211!+12212!+12313!+...=e121.
The first equality holds after cancelling the common terms in the numerator and denominator


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