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hth
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Homework Statement
Let fn(x) = 1/(nx+1) on (0,1) where x is a real number. Show this function does not converge uniformly.
Homework Equations
The Attempt at a Solution
I know why it is not uniformly convergent. Even though fn(x) goes to zero monotonically on the interval (0,1), it's not continuous on a compact interval. How would go about showing this formally/by example?