166 PRINCIPLES OF MATHEMATICAL ANALYSIS 5. Let 10 ( (n+1 sxs) f(x)=sin? х Show that {fn} converges to a continuous funct

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166 PRINCIPLES OF MATHEMATICAL ANALYSIS 5. Let 10 ( (n+1 sxs) f(x)=sin? х Show that {fn} converges to a continuous funct

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166 PRINCIPLES OF MATHEMATICAL ANALYSIS 5. Let 10 ( (n+1 sxs) f(x)=sin? х Show that {fn} converges to a continuous function, but not uniformly. Use the series 2 fn to show that absolute convergence, even for all x, does not imply uni- form convergence.
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