Let [ • denote the greatest integer function and . Then is equal to...

$ n(n+1)(2 n+1)6.3^x<_k=1^n[k^23^x] n(n+1)(2 n+1)6.3^x \\$ $ aligned & _n n(n+1)(2 n+1)6 n^3 3^x< _n 1n^3 _k=1^n[k^23^x] _n n(n+1)(2 n+1)6 3^x n^3 \\ & 13^x+1< _n 1n^3 _k=1^n[k^23^x] 13^x+1 \\ & f(x)=13^x+1 \\ & 12 _j=1^ f(j)=12 _j=1^ 13^j+1=12[19+127+--] \\ & =12 (191-13)=2 aligned$...

Let denote the greatest integer function and f x n arrow: null (Mathematics)

Let [ • denote the greatest integer function and

f(\mathrm{x})=\lim _{\mathrm{n} \rightarrow \infty} \frac{1}{\mathrm{n}^{3}} \sum_{\mathrm{k}=1}^{\mathrm{n}}\left[\frac{\mathrm{k}^{2}}{3^{\mathrm{x}}}\right]

. Then

12 \sum_{\mathrm{j}=1}^{\infty} f(\mathrm{j})

is equal to

\_\_\_\_

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