Question

Tính tổng 1/2.3+1/3.4+......+1/99.100

Answer 1

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

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

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

Answer 2

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

=1/2-1/100 = 49/100

Answer 3

1/2.3 + 1/3.4 + ....+ 1/ 99.100 =99/100

tich ủng hộ nha