Question

Cho \(S=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2011.2012}\)

Tính A = 2012.S

Answer 1

S = 1/2 - 1/3 + 1/3 -1/4 + ......... +1/2011 -1/2012

S= 1/2 - 1/2012 = 1005/2012

Answer 2

\(S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...-\frac{1}{2012}\)

\(S=\frac{1}{2}+0+0+0+...-\frac{1}{2012}\)

\(S=\frac{1}{2}-\frac{1}{2012}\)

\(S=\frac{1005}{2012}\)

\(A=\frac{2012}{1}\cdot\frac{1005}{2012}\)

\(A=1005\)

Answer 3

\(\Leftrightarrow S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{2011}-\frac{1}{2012}\)

\(\Rightarrow S=\frac{1}{2}-\frac{1}{2012}=\frac{1005}{2012}\)

=>A=\(\frac{2012\cdot1005}{1\cdot2012}=\frac{1005}{1}=1005\)