Gọi \(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\)
\(\Rightarrow\frac{1}{2}A=\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\right)\times\frac{1}{2}\)
\(\Rightarrow A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{72}+\frac{1}{90}\)
\(\Rightarrow A=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{9\times10}\)
\(\Rightarrow A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-...+\frac{1}{9}-\frac{1}{10}\)
\(\Rightarrow A=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}\)
\(\Rightarrow A=\frac{2}{5}\div\frac{1}{2}\)
\(\Rightarrow A=\frac{4}{5}\)
1/3+ 1/6 +1/10+...+1/45
= 2/6 + 2/12 + 2/20 +...+ 2/90
= 2/2.3 + 2/3.4 +2/4.5 +...+ 2/9.10
= 2.(1/2 - 1/3 +1/3-1/4 +1/4-1/5+...+1/9-1/10)
= 2. (1/2-1/10)
= 2. 2/5
= 4/5
k nha
Ta có : 1/3 + 1/6 +1/10 +....+ 1/45
= 2/6 + 2/12 + 2/20 +...+2/90
= 2(1/6 + 1/12 + 1/20 +....+1/90)
= 2[1/(2.3) + 1/(3.4) + 1/(4.5)+....+1/(9.10)]
= 2.[ 1/2-1/3+1/3-1/4+1/4-1/5+....+1/9-1/10]
= 2.[1/2 - 1/10]
= 2. 2/5
= 4/5
\(=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{90}\)
\(=\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{9.10}\)
\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=2\times\frac{2}{5}\)
\(=\frac{4}{5}\)
Ta co: 1/3+ 1/6 +1/10+...+1/45
= 2/6 + 2/12 + 2/20 +...+ 2/90
= 2/2.3 + 2/3.4 +2/4.5 +...+ 2/9.10
= 2.(1/2 - 1/3 +1/3-1/4 +1/4-1/5+...+1/9-1/10)
= 2. (1/2-1/10)
= 2. 2/5 = 4/5