Question

Tính tổng   1/1x2 +1/2x3 +1/3x4 +......+1/2010x2011 

Answer 1

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2010\cdot2011}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2010}-\frac{1}{2011}\)

\(=1-\frac{1}{2011}\)

\(=\frac{2010}{2011}\)

Answer 2

1/1x2 + 1/2x3 + 1/3x4 + .... + 1/2010x2011 

=1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2010 - 1/2011 

= 1/1 - 1/2011 

=2010/2011