exponential growth Definition and 1 Threads

  1. L

    ##\lim_{n\to\infty}\left(n\left(1+\frac1n\right)^n-ne\right)=?##

    ##\left(1+\dfrac1n\right)^n=e^{n\ln\left(1+\dfrac1n\right)}## and using Taylor expansion ##\ln\left(1+\dfrac1n\right)=\dfrac 1n-\dfrac1{2n^2}+\dfrac1{3n^3}-\cdots## ##n\ln\left(1+\dfrac1n\right)=1-\dfrac 1{2n}+\dfrac1{3n^2}-\cdots## ##e^{n\ln(1+\frac1n)}=e.e^{-\frac1{2n}+\frac 1{3n^2}-...}##...
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