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lim-n-1-1-n-n-1-1-n-n-e-2-n-2-




Question Number 132138 by benjo_mathlover last updated on 11/Feb/21
 lim_(n→∞) ((((1+(1/n))^n )/((1−(1/n))^n )) − e^2  )n^2 =?
limn((1+1n)n(11n)ne2)n2=?
Answered by EDWIN88 last updated on 11/Feb/21
L=e^2 ×lim_(x→0)  ((ln (1+x)−ln (1−x)−2x)/x^3 )  L=e^2 ×lim_(x→0)  (((1/(1+x))+(1/(1−x))−2)/(3x^2 ))  L=e^2 ×lim_(x→0)  ((2−2(1−x^2 ))/((1+x)(1−x)3x^2 ))  L=e^2 ×lim_(x→0)  ((2x^2 )/(3x^2 )) = ((2e^2 )/3)
L=e2×limx0ln(1+x)ln(1x)2xx3L=e2×limx011+x+11x23x2L=e2×limx022(1x2)(1+x)(1x)3x2L=e2×limx02x23x2=2e23

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