Question

[CÔ NÀNG CỰ GIẢI]

 Tính nhanh:

 S = 1/2x4 + 1/6x8 + 1/8x10 +...+ 1/98x100

Answer 1

[Đoàn Đức Hà]

\(S=\frac{1}{2\times4}+\frac{1}{4\times6}+\frac{1}{6\times8}+...+\frac{1}{98\times100}\)

\(=\frac{1}{2}\times\left(\frac{2}{2\times4}+\frac{2}{4\times6}+\frac{2}{6\times8}+...+\frac{2}{98\times100}\right)\)

\(=\frac{1}{2}\times\left(\frac{4-2}{2\times4}+\frac{6-4}{4\times6}+\frac{8-6}{6\times8}+...+\frac{100-98}{98\times100}\right)\)

\(=\frac{1}{2}\times\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\right)\)

\(=\frac{1}{2}\times\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=\frac{49}{200}\)