9ITS
(xnk/n)n nk/n = 1
so its xn = 0
if n is an infinte integer as
in case of - value of x , (-1)n is defined only for integers
k is a positive integer and | x | < 1
What is \lim_{n \to \infty} xn nk = ?
answer supposd to be 0
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4 Answers
9
9nk/n = eklogn/n
now when n is infinity
logn/n is 0 ( use l'hospitals)
so its virtually e0 = 1
1lim n→∞ xn / n-k
apply L'Hopital rule k times
limit = xn(lnx)k / (-1)kk!
whose limiting value is 0 as n tends to infinity