Giải bài 5 trang 21

Đề bài

Tính nhanh.

$M=\left(100-1\right).\left(100-2^2\right).\left(100-3^2\right)...\left(100-{50}^2\right)$

Lời giải chi tiết

Ta có:

$\begin{array}{c}M=\left({10}^2-1\right).\left({10}^2-2^2\right).\left({10}^2-3^2\right)....\left({10}^2-{10}^2\right)...\left(100-{50}^2\right)\\ =\left({10}^2-1\right).\left({10}^2-2^2\right).\left({10}^2-3^2\right)....0...\left(100-{50}^2\right)\\ =0\end{array}$