Question

1/1x2 + 1/2x3 + 1/3x4 +......+1/98x99 + 1/99x100

Answer 1

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

=1-1/2+1/2-1/3+1/3-1/4+...+1/98-1/99+1/99-1/100

=1-1/100=100/100-1/100=99/100

Answer 2

Ta có: \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)

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

   \(\Rightarrow1-\frac{1}{100}=\frac{99}{100}\)

Answer 3

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

= \(1-\frac{1}{100}=\frac{99}{100}\)