Ta có : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....+\frac{1}{45}\)
\(=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+.....+\frac{2}{90}\)
\(=2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+.....+\frac{1}{90}\right)\)
\(=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{9.10}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{9}-\frac{1}{10}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{10}\right)=1-\frac{1}{5}=\frac{1}{4}\)
Đặt \(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....+\frac{1}{36}+\frac{1}{45}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+....+\frac{1}{72}+\frac{1}{90}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}+\frac{1}{9.10}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{2}-\frac{1}{10}\)
\(\Rightarrow\frac{1}{2}A=\frac{2}{5}\)
\(\Rightarrow A=\frac{2}{5}:\frac{1}{2}\)
\(\Rightarrow A=\frac{2}{5}.2\)
\(\Rightarrow A=\frac{4}{5}\)
1/3 + 1/6 + 1/10 + 1/15 +1/21 +1/28 + 1/36 + 1/45
= 2/6 + 2/12 + 2/20 + 2/30 + 2/42 + 2/56 + 1/72 + 1/90
= 2 . ( 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90
= 2 . ( 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 )
= 2 . ( 1/2 - 1/10 )
= 2 . 2/5
= 4/5
Sorry bạn nha cái kết quả cuối cùng mk viết sai :
Đáng nhẽ : \(1-\frac{1}{5}=\frac{4}{5}\) sửa lại hộ mk nhé !
