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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

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

Grade:12

3 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
10 years ago
f(n)=(10*n+1)/n
f(n)=10+1/n
the largest term i for n=1, which is 11

sher mohammad
b.tech, iit delhi
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
Arjun Premkumar
37 Points
10 years ago
21/2-10.5 31/3-10.3 41/4-10.25 this series dicreasing so 21/2 is greater

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