Question

[Nguyễn Hải Nam]

Tính:

\(\frac{1}{2x4}+\frac{1}{4x6}+\frac{1}{6x8}+..................+\frac{1}{96x98}+\frac{1}{98x100}\)

Nếu giải đúng có lời giải ,sẽ có 2 tick

Answer 1

[Devil]

\(\frac{1}{2x4}+\frac{1}{4x6}+...+\frac{1}{96x98}+\frac{1}{98x199}=\frac{2}{2x4}+\frac{2}{4x6}+...+\frac{2}{99x100}\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...-\frac{1}{100}\)

\(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)

Answer 2

[Học giỏi Math Violympic]

A x2 = \(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+............+\frac{1}{98}-\frac{1}{100}\)

A x2 = \(\frac{49}{100}\)

A = \(\frac{49}{200}\)