\(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+....+\frac{4}{2014.2016}\)
\(=2.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+....+\frac{2}{2014.2016}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+.....+\frac{1}{2014}-\frac{1}{2016}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{2016}\right)\)
\(=2.\frac{1007}{2016}=\frac{1007}{1008}\)
\(A=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2014.2016}\)
\(A=\frac{4}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2014.2016}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2014}-\frac{1}{2016}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{2016}\right)=2.\frac{1007}{2016}=\frac{1007}{1008}\)
A = 4/2.4 + 4/4.6 + 4/6.8 + ... + 4/2014.2016
A = 2.(2/2.4 + 2/4.6 + 2/6.8 + ... + 2/2014.2016)
A = 2.(1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + ... + 1/2014 - 1/2016)
A = 2.(1/2 - 1/2016)
A = 2.1/2 - 2.1/2016
A = 1 - 1/1008
A = 1007/1008
B = 1/18 + 1/54 + 1/108 + ... + 1/990
B = 1/9.(1/2 + 1/6 + 1/12 + ... + 1/110)
B = 1/9.(1/1.2 + 1/2.3 + 1/3.4 + ... + 1/10.11)
B = 1/9.(1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/10 - 1/11)
B = 1/9.(1 - 1/11)
B = 1/9.10/11
B = 10/99
\(A=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2014.2016}\)
\(A:2=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2014.2016}\)
\(A:2=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2014}-\frac{1}{2016}\)
\(A:2=\frac{1}{2}-\frac{1}{2016}=\frac{1007}{2016}\)
\(A=\frac{1007}{2016}:2=\frac{1007}{4032}\)
\(B=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)
\(B=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{30.33}\)
\(B.3=\frac{3}{3.6}+\frac{3}{6.9}+\frac{3}{9.12}+...+\frac{3}{30.33}\)
\(B.3=\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{30}-\frac{1}{33}\)
\(B.3=\frac{1}{3}-\frac{1}{33}=\frac{10}{33}\)
\(B=\frac{10}{33}:3=\frac{10}{99}\)
\(B=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+.....+\frac{1}{990}\)
\(=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+....+\frac{1}{30.33}\)
\(\Rightarrow3B=\frac{3}{3.6}+\frac{3}{6.9}+\frac{3}{9.12}+....+\frac{3}{30.33}\)
\(\Rightarrow#B=\)
\(B=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+,...+\frac{1}{990}\)
\(B=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{30.33}\)
\(B=\frac{1}{3}\left(\frac{3}{3.6}+\frac{3}{6.9}+...+\frac{3}{30.33}\right)\)
\(B=\frac{1}{3}\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+...+\frac{1}{30}-\frac{1}{33}\right)\)
\(B=\frac{1}{3}\left(\frac{1}{3}-\frac{1}{33}\right)=\frac{1}{3}.\frac{10}{33}=\frac{10}{99}\)
\(A=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2014.2016}\)
\(A=2.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2014.2016}\right)\)
\(A=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2014}-\frac{1}{2016}\right)\)
\(A=2.\left(\frac{1}{2}-\frac{1}{2016}\right)\)\(=2.\frac{1007}{2016}=\frac{1007}{1008}\)
A= 2.( 2/2.4 + 2/4.6 + 2/6.8 +...+ 2/2014.2016 )
A= 2.(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2014+1/2016 )
A= 2.(1/2-1/2016)
A= 2.(1008/2016-1/2016)
A= 2.1007/2016
A=1007/1008
Câu B như sai đề ý! Bạn xem lại đề đi
\(A=\frac{1007}{1008}\)
\(B=\frac{10}{99}\)
