Question

tinh

1/1.2+1/2.3+....+1/99.100

Answer 1

Ta có:1/1.2+1/2.3+...+1/99.100

       =1-1/2+1/2-1/3+...+1/99-1/100

       =1-1/100

       =100-1/100

       =99/100

Answer 2

d/s=99/100 

Answer 3

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

\(=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{100-99}{99.100}\)

\(=\frac{2}{1.2}-\frac{1}{1.2}+\frac{3}{2.3}-\frac{2}{2.3}+....+\frac{100}{99.100}-\frac{99}{99.100}\)

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

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