If f(x)=lt n-infinite ([x^2]+[(2x)^2]+[(4x)^2]+...+[(nx)^2]/n^3,prove that f(x) is a continuous function.[] is GIF

Question

If f(x)=lt n->infinite ([x^2]+[(2x)^2]+[(4x)^2]+...+[(nx)^2]/n^3,prove that f(x) is a continuous function.[] is GIF

Arun Kumar · Answer

The fractional part is because max value of {} is 1 so lim =0 Now its clear that the function is continuos. Arun Kumar IIT Delhi Askiitians Faculty

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If f(x)=lt n->infinite ([x^2]+[(2x)^2]+[(4x)^2]+...+[(nx)^2]/n^3,prove that f(x) is a continuous function.[] is GIF

If f(x)=lt_n->infinite([x^2]+[(2x)^2]+[(4x)^2]+...+[(nx)^2]/n^3,prove that f(x) is a continuous function.[] is GIF

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If f(x)=lt n->infinite ([x^2]+[(2x)^2]+[(4x)^2]+...+[(nx)^2]/n^3,prove that f(x) is a continuous function.[] is GIF

If f(x)=ltn->infinite ([x^2]+[(2x)^2]+[(4x)^2]+...+[(nx)^2]/n^3,prove that f(x) is a continuous function.[] is GIF

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If f(x)=lt_n->infinite([x^2]+[(2x)^2]+[(4x)^2]+...+[(nx)^2]/n^3,prove that f(x) is a continuous function.[] is GIF