Question

1/2+1/6+1/12+......+1/110                                                                                                                   

Answer 1

\(=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{10\cdot11}\)

=1-1/2+1/2-1/3+1/3-1/4+...+1/10-1/11

=1-1/11=10/11

Answer 2

\(=\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{10.11}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\)

\(=1-\dfrac{1}{11}=\dfrac{10}{11}\)

Answer 3

Tham khảo
 = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + ... + 1/110

 = 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7 + .... + 1/10x110

 = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/10 - 1/11

 = 1 - 1/11

 = 10/11

Answer 4

^{_{\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\cdot\cdot\cdot+\dfrac{1}{110}\)}}

 

^{_{\(=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\cdot\cdot\cdot+\dfrac{1}{10\cdot11}\)}}

 

^{_{\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\cdot\cdot\cdot+\dfrac{1}{10}-\dfrac{1}{11}\)}}

 

^{_{\(=1-\dfrac{1}{11}\)}}

 

^{_{\(=\dfrac{10}{11}\)}}