Question

[Cỏ dại]

Tính : 

\(\frac{2}{1.2.3}\) + \(\frac{2}{2.3.4}\) + \(\frac{2}{3.4.5}\) + ... + \(\frac{2}{98.99.100}\)

Chiều là mình phải nộp rồi!

Answer 1

[perfect shadow]

= 1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + .....+1/98.99 - 1/99.100

= 1/2 - 1/9900

= 4949/9900

k cho minh nha

chuc ban hoc tot

Answer 2

[TXT Channel Funfun]

\(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{98.99.100}\)

\(=2.\frac{1}{1.2.3}+2.\frac{1}{2.3.4}+...+2.\frac{1}{98.99.100}\)

\(=2.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{98.99.100}\right)\)

\(=2.\left[\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\frac{1}{2}.\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+...+\frac{1}{2}.\left(\frac{1}{98.99}-\frac{1}{99.100}\right)\right]\)

\(=2.\left[\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{98.99}-\frac{1}{99.100}\right)\right]\)

\(=2.\left[\frac{1}{2}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\right]\)

\(=2.\left[\frac{1}{2}.\left(1-\frac{1}{100}\right)\right]\)

\(=2.\left(\frac{1}{2}.\frac{99}{100}\right)\)

\(=\left(2.\frac{1}{2}\right).\frac{99}{100}\)

\(=1.\frac{99}{100}\)

\(=\frac{99}{100}\)