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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 calculas

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 calculas

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
lim n->infinity n^1/n
let A=lim n->infinity n^1/n
taking log on both sides
log A=lim n->infinity (logn)/n form infinity/infinity
Using L'Hospital rule
logA=lim n->infinity (1/n)/1
=>logA=limn->infinity(1/n)
=>logA=1/infinity=0
=>A=e^0=1
Hence gthe largest Term in this sequence is 1.
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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