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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:12

1 Answers

Varun Sharma
18 Points
7 years ago
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

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