Question

Tính nhanh

a) S= 1-2+3-4+5-6+...+2001-2002+2003

b) \(A=\frac{12}{3.5}+\frac{12}{5.7}+...+\frac{12}{2013.2015}\)

Answer 1

\(A=\frac{12}{3.5}+\frac{12}{5.7}+...+\frac{12}{2013.2015}\)

\(2A=\frac{24}{3.5}+\frac{24}{5.7}+...+\frac{24}{2013.2015}\)

\(2A=\frac{24}{3}-\frac{24}{5}+\frac{24}{5}-\frac{24}{7}+...+\frac{24}{2013}-\frac{24}{2015}\)

\(2A=8-\frac{24}{2015}\)

\(2A=\frac{8}{1}-\frac{24}{2015}\)

\(2A=\frac{16120}{2015}-\frac{24}{2015}\)

\(2A=\frac{16096}{2015}\)

\(=>A=\frac{16096}{2015}:2\)

\(=>A=\frac{16096}{4030}\)