=1/1x2+1/2x3+1/3x4+1/4x5+1/5x6
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1/1-1/6
=6/6-1/6
=5/6
Dùng từ xưng hô không hợp lý nhé :D
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=1-\frac{1}{6}=\frac{5}{6}\)
\(=\frac{30}{60}+\frac{10}{60}+\frac{5}{60}+\frac{3}{60}+\frac{2}{60}\)
\(=\frac{30+10+5+3+2}{60}=\frac{50}{60}=\frac{5}{6}\)
chia các phép tinh trên thành 2 nhóm , ta có:
(1/2+1/6+1/12)+(1/20+1/30)
=(6/12+2/12+1/12)+(3/60+2/60)
=9/12+5/60
=9/12+1/12
=10/12
=5/6
Kết quả = 5/6