2010/017) Lim (n -> infinity) {(1 + 1/n)^n - (1 + 1/n)}^-n is

(a) 1; (b) 1/(e - 1); (c) 1 - e^-1; (d) 0;?

Ans:
take (1+1/n) out to get

(1+1/n)^-n((1+1/n)^(n-1)-1)^-n

as n->infinite (1+1/n)^-n = 1/e

((1+1/n)^(n-1)-1)^(-n) = (e-1)^(-n) = 0

so product = 0

hence d