=438.(1/111.113+1/113.113+...+1/217.219)
=438.1/2.(2/111.113+2/113.115+...+1/217.219)
=438.1/2.(1/111-1/113+1/113-1/115+...+1/217-1/219)
=438.1/2.(1/111+0+0+..+0-1/219)
=438.1/2.(1/111-1/219)=219/111-1=
b tự tính
\(A=\frac{438}{111.113}+\frac{438}{113.115}+\frac{438}{115.117}+...+\frac{438}{217.219}\)
\(A=219\left(\frac{2}{111.113}+\frac{2}{113.115}+\frac{2}{115.117}+...+\frac{2}{217.219}\right)\)
\(A=219\left(\frac{1}{111}-\frac{1}{113}+\frac{1}{113}-\frac{1}{115}+\frac{1}{115}-\frac{1}{117}+...+\frac{1}{217}-\frac{1}{219}\right)\)
\(A=219\left(\frac{1}{111}-\frac{1}{219}\right)\)
