=1/1-1/2+1/2-1/4+...+1/46-1/56
=1-1/56
55/56
\(P=\frac{1}{1\cdot2}+\frac{2}{2\cdot4}+\frac{3}{4\cdot7}+...+\frac{10}{46\cdot56}\)
\(\Rightarrow P=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{46}-\frac{1}{56}\)
\(\Rightarrow P=1-\frac{1}{56}\)
\(\Rightarrow P=\frac{55}{56}\)
\(P=\frac{1}{1.2}+\frac{2}{2.4}+\frac{3}{4.7}+...+\frac{10}{46.56}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{46}-\frac{1}{56}\)
\(=1-\frac{1}{56}\)
\(=\frac{55}{56}\)
Vậy \(P=\frac{55}{56}\)