Consider the infinite sequence {n1/n } i.e. 1 , 21/2 , 31/3 . . . . .Find the largest term in this sequence(if it exists). Hint: Use Calculus

nth term of the sequence is given by : (10n + 1)/n for n>1
Differentiate it : 0 - 1/n^2
It is always less than 0. Hence, it is decreasing always.
Hence, the largest term is 21/2.
Thanks
Bharat Bajaj