1. Mathematics
2. Calculus and Analysis
3. Real Analysis
4. 30029

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Taking the continuity of h(x) as given in#30026,#30028
by using any of the functional limits and continuity theorems prove that the finite sum g_m (x)=sum sign(oo top n=0 bottom) of 1/2^n h(2^n x) is continous on R