Tính tổng

C

- Hướng dẫn giải

Đáp án C

Ta có $\left\{\begin{array}{l}\left\{\begin{array}{l}{2}^2.{\log }_{\sqrt{2}}2=2^3.{\log }_{2}2=2^3\\ 3^2.{\log }_{\sqrt{2}}2=3^3.{\log }_{2}2=3^3 suy ra S=1^3+2^3+3^3+...+{2017}^3\end{array}\right.\\ ........\end{array}\right.$ 

Mà $x^3={\left[\frac{x\left(x+1\right)}{2}\right]}^2-{\left[\frac{x\left(x-1\right)}{2}\right]}^2\Rightarrow S=1^3+2^3+...+n^3={\left[\frac{n\left(n+1\right)}{2}\right]}^2={1009}^2.{2017}^2.$