\(A=\frac{1}{30}+\frac{1}{42}+...+\frac{1}{210}\)
\(A=\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{14.15}\)
\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{14}-\frac{1}{15}\)
\(A=\frac{1}{5}-\frac{1}{15}\)
Tự tính nha :)
\(B=\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{99.100}\)
\(B=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)
\(B=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)
\(B=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(B=2\left(\frac{1}{2}-\frac{1}{100}\right)\)
Tự làm
\(A=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+....+\frac{1}{210}\)
\(\Rightarrow A=\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+....+\frac{1}{14\cdot15}\)
\(\Rightarrow A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+......+\frac{1}{14}-\frac{1}{15}\)
\(\Rightarrow A=\frac{1}{5}-\frac{1}{15}\)
\(\Rightarrow A=\frac{2}{15}\)
\(B=\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+\frac{2}{4\cdot5}+....+\frac{2}{99\cdot100}\)
\(\Rightarrow B=2\cdot\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+....+\frac{1}{99\cdot100}\right)\)
\(\Rightarrow B=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{100}\right)\)
\(\Rightarrow B=2\cdot\left(\frac{1}{2}-\frac{1}{100}\right)\)
\(\Rightarrow B=2\cdot\frac{49}{100}\)
\(\Rightarrow B=\frac{49}{50}\)