Let f_{n} (x) = x^{n}\forallx [0,1] and for all positive integers n, then

Correct Answer is : fn converges at every point but does not converge uniformly

f_{n} does not converge at any point

f_{n} converges at every point but does not converge uniformly

f_{n} converges at some points but does not converges at some other points

AAI ATC Junior Executive 26 Dec 2015 Shift 1 Paper

Question : 97 of 120

Marks: +1, -0

Let

f_{n} (x) = x^{n}∀x [0,1]

and for all positive integers n, then

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