1/2=1/1.2
1/6=1/2.3
1/12=1/3.4
1/20=1/4.5
1/30=1/5.6
1/42=1/6.7
ta có 1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7
= 1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1/1-1/7
=6/7
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
\(=1-\frac{1}{7}\)
\(=\frac{6}{7}\)
\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+\frac{1}{6x7}\)
=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-....-\frac{1}{7}\)
=\(1-\frac{1}{7}\)=\(\frac{6}{7}\)
1/2 + 1/6 + 1/ 12 + 1/ 30 + 1/42 = (1/2 + 1/6 + 1/12) + (1/42 + 1/30 + 1/20) = (6/12 + 2/12 + 1/12)+(10/420 + 14/420 + 21/420 )
= 9/12 + 45/420 = 9/12 + 3/28 = 56/84 + 9/84 = 65/84
