+91-87964 74404
FlagBACK
Question icon
Grade Upto college levelAlgebra

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)

Profile image of Narasimha Reddy
12 Years agoGrade Upto college level
Answers icon

1 Answer

Profile image of Sher Mohammad
12 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

Other Related Questions on algebra

question mark
What is a binomial expression?
algebra
1 Answer Available

Last Activity: 2 Years ago

question mark
Can we divide two vectors? If this is possible then how?
algebra
1 Answer Available

Last Activity: 2 Years ago

question mark
How do you write “the product of 18 and q” as an algebraic expression?
algebra
1 Answer Available

Last Activity: 2 Years ago

question mark
दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे
algebra
1 Answer Available

Last Activity: 3 Years ago

question mark
Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?
algebra
1 Answer Available

Last Activity: 3 Years ago