Question

tính 1/2.3+1/3.4+1/4.5+......+1/99.100

Answer 1

1/2.3+1/3.4+1/4.5+...+1/99.100

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

=\(\frac{1}{2}-\frac{1}{100}=\frac{50}{100}-\frac{1}{100}=\frac{49}{100}\)

Answer 2

=1/2-1/3+1/3-1/4+1/4-1/5+......+1/99-1/100

=1/2-1/100

=49/100