Gọi biểu thức trên là A, ta có:
\(A=\frac{1}{2\cdot15}+\frac{1}{15\cdot3}+\frac{1}{3\cdot21}+\frac{1}{21\cdot4}+...+\frac{1}{87\cdot90}\)
\(13A=\frac{13}{2\cdot15}+\frac{13}{15\cdot3}+\frac{13}{3\cdot21}+\frac{13}{21\cdot4}+...+\frac{13}{87\cdot90}\)
\(13A=\frac{1}{2}-\frac{1}{15}+\frac{1}{15}-\frac{1}{3}+\frac{1}{3}-\frac{1}{21}+\frac{1}{21}-\frac{1}{4}+...+\frac{1}{87}-\frac{1}{90}\)
\(13A=\frac{1}{2}-\frac{1}{90}\)
\(13A=\frac{22}{45}\)
\(A=\frac{22}{45\text{x}13}=\frac{22}{585}\)