\(S=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2010.2011}\)
\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2010}-\frac{1}{2011}\)
\(S=1-\frac{1}{2011}\)
\(S=\frac{2010}{2011}\)
Phân tích: 1 / 1 x 2 = 1 - 1/2
1/2.3 = 1/2 - 1/3
. ....Bạn làm tương tự các số còn lại...
Ta được: 1 - 1/2 + 1/2 - 1/3 + ....+1/ 2010 - 1/2011
= 1 - 1/2011
= 2010/2011
\(S=\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{2010\times2011}\)
\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2010}-\frac{1}{2011}\)
\(S=1-\frac{1}{2011}\)
\(S=\frac{2010}{2011}\)
S=1-1/2+1/2-1/3+...+1/2010-1/2011
S=1-1/2011
S=2010/2011