Question

chứng minh rằng a/n(n+a) =1/n -1/n+a (n ,a thuộc N*)

Tính A= 1/2.3 +1/3.4+..........+1/99.100

Answer 1

\(\frac{a}{n\left(n+a\right)}\)

=\(\frac{\left(n+a\right)-n}{n\left(n+a\right)}\)

=\(\frac{n+a}{n\left(n+a\right)}\)\(-\frac{n}{n\left(n+a\right)}\)

Rút gọn, ta được:

\(\frac{1}{n}\)\(-\frac{1}{n+a}\)

=>đpcm

 

A=\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

A=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

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

A=\(\frac{50}{100}-\frac{1}{100}\)

A=\(\frac{49}{100}\)