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1/1x2 + 1/2x3 + 1/3x4 +1/4x5 +1/5x6

= 1 -1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6

= 1 - 1/6 = 5/6

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{5\cdot6}=\left(\frac{1}{1}-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+...+\left(\frac{1}{5}-\frac{1}{6}\right)=1-\frac{1}{6}=\frac{5}{6}.\)

= 1- 1/2+1/2-1/3+...+1/5-1/6

=1-1/6

=5/6

=1-1/2+1/2-1/3+...+1/5-1/6

=1-1/6

=5/6

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=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6

=1-1/6

=5/6

\(\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)-\)\(\left(\frac{1}{5}-\frac{1}{6}\right)\)

1-1/6= 5/6

tích nhá

a.1/7 + 2/7 + 3/7 + 4/7 + 5/7 + 6/7 = ( 1/7+6/7) + ( 2/7+5/7) + (3/7+4/7)

                                                   = 1 + 1 + 1 

                                                   = 3

b. = 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6     ( loại bỏ các p/s giống nhau)

   = 1/1 - 1/6

  = 5/6 

a. Các phân số bé hơn 1 có mẫu số bằng 7 là: \(\frac{1}{7};\frac{2}{7};\frac{3}{7};\frac{4}{7};\frac{5}{7};\frac{6}{7}\)

Ta có : \(\frac{1}{7}+\frac{2}{7}+\frac{3}{7}+\frac{4}{7}+\frac{5}{7}+\frac{6}{7}\)

\(=\frac{1+2+3+4+5+6}{7}=\frac{21}{7}=3\)

b. \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)

\(=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+\frac{6-5}{5.6}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

\(=\frac{1}{1}-\frac{1}{6}\)

\(=\frac{5}{6}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{5.6}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{5}-\frac{1}{6}\)

\(=1-\frac{1}{6}\)

\(=\frac{5}{6}\)

\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}\)

=>\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

=> 1-\(\frac{1}{6}\)

=\(\frac{6}{6}-\frac{1}{6}=\frac{6}{6}+\frac{-1}{6}=\frac{5}{6}\)