Question

1/2*4cộng1/4*6cộng1/6*8cộng..........cộng1/96*98cộng1/98*100bằng bao nhiêu các bạn?

Answer 1

Gọi số đó là A

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

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

A x 2 = \(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-...-\frac{1}{96}+\frac{1}{96}-\frac{1}{98}+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)A x 2 = \(\frac{1}{2}-\frac{1}{100}\) = \(\frac{49}{100}\)

A = \(\frac{49}{100}\): 2 = \(\frac{49}{200}\)

           Đáp số: \(\frac{49}{200}\)

Answer 2

$\frac{49}{200}$