dễ thôi
1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90
= 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10
= 1/2 - 1/3 +1/3 - 1/4 + 1/4 - 1/5 + ...+ 1/9 - 1/10
= 1/2 - 1/10
= 2/5
/ là dâu gạch ps nha
d=1/2.3+1/3.4+1/4.5+11/5.6+1/6.7+1/7.8+1/8.9+1/9.10 D=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10 D=1/2-1/10=2/5
D=1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90
D= 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10
F= 1/2 - 1/3 +1/3 - 1/4 + 1/4 - 1/5 + ...+ 1/9 - 1/10
D= 1/2 - 1/10
D= 2/5
\(D=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)
\(=1-\frac{1}{10}=\frac{9}{10}\)
Ta có :
6 = 2.3
12 = 3.4
20 = 4.5
...
90 = 9.10
=>
\(D=\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)
\(D=\frac{1}{1}.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(D=\frac{1}{1}.\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(D=\frac{1}{1}.\left(\frac{2}{5}\right)\)
\(D=\frac{2}{5}\)
