Question

[Trà Bonnie]

Tìm A biết ;
   A = 1/7 + 1/91 + 1/247 + .... + 1/1147

Answer 1

[Hà Phương]

\(A=\frac{1}{7}+\frac{1}{91}+\frac{1}{247}+...+\frac{1}{1147}\)

\(A=\frac{1}{1.7}+\frac{1}{7.13}+\frac{1}{13.19}+....+\frac{1}{31.37}\)

\(A=\frac{6}{6}\left(\frac{1}{1.7}+\frac{1}{7.13}+\frac{1}{13.19}+...+\frac{1}{31.37}\right)\)

\(A=\frac{1}{6}\left(\frac{6}{1.7}+\frac{6}{7.13}+\frac{6}{13.19}+...+\frac{6}{31.37}\right)\)

\(A=\frac{1}{6}\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{19}+....+\frac{1}{31}-\frac{1}{37}\right)\)

\(A=\frac{1}{6}\left(1-\frac{1}{37}\right)\)

\(A=\frac{1}{6}.\frac{36}{37}=\frac{6}{37}\)

Answer 2

[Đinh Tuấn Việt]

\(A=\frac{1}{6}.\left(\frac{6}{1.7}+\frac{6}{7.13}+\frac{6}{13.19}+...+\frac{6}{31.37}\right)\)

    \(=\frac{1}{6}.\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+...+\frac{1}{31}-\frac{1}{37}\right)\)

    \(=\frac{1}{6}.\left(1-\frac{1}{37}\right)=\frac{1}{6}.\frac{36}{37}=\frac{6}{37}\)