Question

1/3+1/15+1/35+.....+1/195

Answer 1

 A= 1/1.3+1/3.5+1/5.7+...+1/13.15

2A=2/1.3+2/3.5+2/5.7+...+2/13.15

2A=1-1/3+1/3-1/5+1/5-1/7+...+1/13-1/15

2A=1-1/15

2A=14/15

A=7/15

Answer 2

bạn tách mẫu ra mà giải bạn .... naturo làm đúng rồi đó

Answer 3

Đặt \(A=\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{195}\)

\(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{13.15}\)

\(A=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}\right)\)

\(A=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)\)

\(A=\frac{1}{2}.\left(1-\frac{1}{15}\right)\)

\(A=\frac{1}{2}.\frac{14}{15}=\frac{7}{15}\)

Answer 4

\(A=\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{195}\) 

\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}\) 

\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{13}-\frac{1}{15}\) 

\(2A=1-\frac{1}{15}=\frac{14}{15}\) 

\(A=\frac{14}{15}.\frac{1}{2}=\frac{7}{15}\)