Science & Mathematics » Mathematics » F_n(x) is a real-valued function defined on [0, 1] by the formula below. Prove that {f_n} converges pointwise.?

F_n(x) is a real-valued function defined on [0, 1] by the formula below. Prove that {f_n} converges pointwise.?

f_n= 0 if 0<= x <2^(-n)
= 2^(n/2) if 2^(-n)<= x <= 2^(1-n)
= 0 if 2^(1-n)< x <= 1

I'm supposed to prove that {f_n} converges pointwise to 0 but the limit f_n doesn't equal 0.

I get that when x is between 2^-n and 2^(1-n), the interval is shrinking and shifting to the left as n approaches infinity. My TA gave me a hint that I'm supposed to show that given any x, I can find N such that for n>N the interval will not include x. I still need more help with solving this problem, though...

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