Tìm tổng

Câu hỏi: Tìm tổng $S=1+2^2{\log }_{\sqrt{2}}2+3^2{\log }_{\sqrt[3]{2}}2+4^2{\log }_{\sqrt[4]{2}}2+{2017}^2{\log }_{\sqrt[2017]{2}}2$ 

A. $S={1008}^2.{2017}^2$

B. $S={1007}^2.{2017}^2$

C. $S={1009}^2.{2017}^2$

D. $S={1010}^2.{2017}^2$