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Grade: 12
        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
6 years ago

Answers : (1)

Varun Sharma
18 Points
							f(x) = x^1/x
=e^((lnx)/x)
f`(x)=0
hence ln x=1
or x=e

f`(x) has maxima at e
nearest integers are 2 nd 3...
consider 
2^1/2 nd 3^1/3
take power 6 both the sides 
2^3<3^2
therefore 
3^1/3 > 2^1/2
hence greatest x=3
						
6 years ago
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