Question

\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+.....+\frac{1}{2009x2010}+\frac{1}{2010x2011}\) 

Mấy bạn giúp mình nhé , mình  đang gấp , 9h mình cần rồi , nhớ giải chi tiết nhé , thanks nhiều ( sẽ hậu tạ ) 

Answer 1

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

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

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

Answer 2

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

= 1 - 1/2011

= 2010/ 2011

Đáp số: 2010/2011

Chúy ý công thức: \(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)

Answer 3

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

= 1 - 1/2011

= 2010/2011

Đáp sô: 2010/2011

Chú ý công thưc:              \(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)

Answer 4

\(\frac{1}{1x2}\)+\(\frac{1}{2x3}\)+ \(\frac{1}{3x4}\)+ .......+ \(\frac{1}{2009x1010}\) +\(\frac{1}{2010x2011}\)

1 - \(\frac{1}{2}\)+ \(\frac{1}{2}\)- \(\frac{1}{3}\)+ \(\frac{1}{3}\)- \(\frac{1}{4}\)+ ....... + \(\frac{1}{2009}\)- \(\frac{1}{2010}\)+ \(\frac{1}{2010}\)- \(\frac{1}{2011}\)

1 - \(\frac{1}{2011}\)= \(\frac{2010}{2011}\)

k nhé

Answer 5

\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+.......+\frac{1}{2009x2010}+\frac{1}{2010x2011}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{2009}-\frac{1}{2010}+\frac{1}{2010}-\frac{1}{2011}\)

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

 \(=\frac{2010}{2011}\)