Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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 ( please show in a paper)

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 ( please show in a paper)

Grade:Upto college level

1 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
7 years ago
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

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free