\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+..........+\frac{1}{132}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+..........+\frac{1}{11.12}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...........+\frac{1}{11}-\frac{1}{12}\)

\(=1-\frac{1}{12}\)

\(=\frac{11}{12}\)

bài này hóc búa thật

hơi khó 5 chút

Bài làm 

\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}+\frac{1}{110}\)

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{9.10}+\frac{1}{10.11}\)

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)

\(A=\frac{1}{1}-\frac{1}{11}\)

\(A=\frac{10}{11}\)

Bằng \(\frac{9}{22}\)nha bạn.

\(\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{10.11}\)

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

=\(\frac{1}{2}-\frac{1}{11}\)

=\(\frac{9}{22}.\)

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}+\frac{1}{110}\)

\(=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+...+\frac{1}{9\times10}+\frac{1}{10\times11}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-...-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)

\(=\frac{1}{2}-\frac{1}{11}\)

\(=\frac{9}{22}\)

1/12+1/20+1/30+...+1/90+1/110

=1/3.4+1/4.5+1/5.6+...+1/9.10+1/10.11

=1/3-1/4+1/4-1/5+1/5-1/6+...+1/9-1/10+1/10-1/11

=1/3-1/11

=8/33

1/12+1/20+1/30+...+1/90+1/110

=1/3.4+1/4.5+1/5.6+...+1/9.10+1/10.11

=1/3-1/4+1/4-1/5+1/5-1/6+...+1/9-1/10+1/10-1/11

=1/3-1/11

=8/33

Đặt tổng trân là A

Ta có A=1/2x3+1/3x4+...+1/10x11

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

Sau khi rút gọn ta được A=1/2-1/11

A=9/22

bằng 10/11

đúng nhớ **** cho minh nha

1 + 1 = 11 / 2 + 2 = 22

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T-T

ta có:

1/6+1/12+1/20+1/30+.........+1/90+1/110

= 1/2x3+1/3x4+1/4x5+1/5x6+....+1/9x10+1/10x11

= 1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+....+1/9-1/10+1/10-1/11

=1/2-1/11=11/22-2/22=9/22

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)
\(=\left(\frac{1}{2}-\frac{1}{11}\right)+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+...+\left(\frac{1}{10}-\frac{1}{10}\right)\)
\(=\frac{1}{2}-\frac{1}{11}=\frac{11}{22}-\frac{2}{22}=\frac{9}{22}\)

  \(\frac{1}{2}\) + \(\frac{1}{6}\) + \(\frac{1}{12}\) + ............ + \(\frac{1}{90}\) + \(\frac{1}{110}\) 

= \(\frac{1}{1.2}\) + \(\frac{1}{2.3}\) + \(\frac{1}{3.4}\) + ............ + \(\frac{1}{9.10}\) + \(\frac{1}{10.11}\)

= 1 - \(\frac{1}{2}\) + \(\frac{1}{2}\) - \(\frac{1}{3}\) + \(\frac{1}{3}\) - \(\frac{1}{4}\) + ................. + \(\frac{1}{9}\) - \(\frac{1}{10}\) + \(\frac{1}{10}\) - \(\frac{1}{11}\)

= 1 - \(\frac{1}{11}\) 

= \(\frac{10}{11}\)

\(A=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{10}-\frac{1}{11}=\frac{1}{2}-\frac{1}{11}=\frac{9}{22}\)

=1/2.3+1/3.4+1/4.5+......+1/10.11

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

=1-1/11

=10/11

Tick