\(S=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{13.15}\)
\(\Rightarrow S=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{13}-\frac{1}{15}\right)\)
\(\Rightarrow S=\frac{1}{2}.\left(1-\frac{1}{15}\right)\)
\(\Rightarrow S=\frac{1}{2}.\frac{14}{15}\)
\(\Rightarrow S=\frac{7}{15}\)
\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+....+\frac{1}{195}\)
\(=\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+...+\frac{1}{13x15}\)
\(=\frac{1}{2}x\left(\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+\frac{2}{7x9}+...+\frac{2}{13x15}\right)\)
\(=\frac{1}{2}x\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{13}-\frac{1}{15}\right)\)
\(=\frac{1}{2}x\left(1-\frac{1}{15}\right)=\frac{1}{2}x\frac{14}{15}=\frac{7}{15}\)
\(\frac{1}{3}\)+\(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+...+\)\(\frac{1}{195}\)
=\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{13.15}\)
=(\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{13}-\frac{1}{15}\)) :2
=\(\left(1-\frac{1}{15}\right)\):2
=\(\frac{14}{15}:2\)
=\(\frac{7}{15}\)
mk giải đúng ko vậy , sai thì nói ra mk còn sửa nha
Đặt \(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+...+\frac{1}{195}\)= A
A = \(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+...+\frac{1}{195}\)
A = \(\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+...+\frac{1}{13x15}\)
A x 2 = \(\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+\frac{2}{7x9}+...+\frac{2}{13x15}\)
A x 2 = \(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{13}-\frac{1}{15}\)
A x 2 = 1 - \(\frac{1}{15}=\frac{14}{15}\)
A = \(\frac{14}{15}:2=\frac{7}{15}\)
Đáp số: \(\frac{7}{15}\)
\(\text{Đặt:}\)\(A=\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+...+\frac{1}{195}\)
\(\Leftrightarrow A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+.....+\frac{1}{13.15}\)
\(\Rightarrow2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+.....+\frac{2}{13.15}\)
\(\Rightarrow2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.......+\frac{1}{13}-\frac{1}{15}\)
\(\Rightarrow2A=1-\frac{1}{15}\)
\(\Rightarrow2A=\frac{14}{15}\)
\(\Rightarrow A=\frac{14}{15}:2=\frac{7}{15}\)
