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Space of continuous functions

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Let C[0,1] be the space of continuous real functions where C[0,1] has the following norm
||f||_2 =( integral (from 0 to 1) |f(t)|dt)^(1/2)

Consider f_n(t) = 0
for t greater than or equal to zero and less than or equal to 1/2-1/n,
f_n(t)=1+n(t-1/2) for t great than or equal to 1/2-1/n and t less than or equal to 1/2
and f_n(t)=1 when t is greater than or equal to 1/2 and t less than or equal to 1

Is {f_n} convergent in (C[0,1].||.||)? Justify your answer

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Space of continuous functions is inspected.

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