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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 calculus

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

Grade:Upto college level

2 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
10 years ago 
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
askiitians faculty
IIT Delhi

PERUMAL
37 Points
10 years ago
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.

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