Consider the infinite sequence {n^1/n } i.e. 1, 2^1/2 , 3^1/3 . . . . .Find the largest term in this sequence(if it exists). HINT:USE CALCULUS

f(n)= n^(1/n)
log(f(n))= log(n)/n
taking derivative both sides
f'(n)/f(n)= (1/(n^2)-log(n)/(n^2)
f'(n)=(1-log(n))f(n)/n^2

f'(n)=0 log(n)=1,
n=e , which imply nearest integer is 3,

for n=3 , the function has maxima

sher mohammad
b.tech, iitd delhi