Coi: \(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{36}+\frac{1}{45}\)
\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{72}+\frac{1}{90}\)
\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}+\frac{1}{9.10}\)
\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\)
\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{2}-\frac{1}{10}=\frac{13}{20}\)
\(\frac{1}{2}A\times2=A=2\times\frac{13}{20}=\frac{13}{10}\)
\(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.....+\frac{1}{36}+\frac{1}{45}\)
\(=\frac{1}{2}+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+.....+\frac{2}{72}+\frac{2}{90}\)
\(=\frac{1}{2}+2.\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{72}+\frac{1}{90}\right)\)
\(=\frac{1}{2}+2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(=\frac{1}{2}+2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
\(=\frac{1}{2}+2.\left(\frac{1}{2}-\frac{1}{10}\right)=\frac{1}{2}+2.\frac{2}{5}=\frac{1}{2}+\frac{4}{5}=\frac{13}{10}\)
\(\frac{A}{2}=1+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}\)
\(\frac{A}{2}=1+\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(\frac{A}{2}=1+\left(\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+\frac{6-5}{5.6}+...+\frac{9-8}{8.9}+\frac{10-9}{9.10}\right)\)
\(\frac{A}{2}=1+\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
\(\frac{A}{2}=1+\frac{1}{2}-\frac{1}{10}=\frac{14}{10}\Rightarrow A=\frac{14}{5}=2,8\)
Đặt \(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{36}+\frac{1}{45}\)
\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{72}+\frac{1}{90}\)
\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}+\frac{1}{9.10}\)
\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\)
\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{2}-\frac{1}{10}=\frac{13}{20}\)
\(\frac{1}{2}A\times2=A=2\times\frac{13}{20}=\frac{13}{10}\)
Thang Thien Ngoai Phi Tien copy bai Nguyen Hoang Tien kia, khong lam duoc thi cu thich copy. Xau tinh v.