A=1/4*5 + 1/5*6 + 1/6*7 +.....+1/99*100

A=1/4-1/5+1/5-1/6+1/6-1/7+...+1/99-1/100

A=1/4-1/100

A=25/100-1/100

A=6/25

A = 1/20 + 1/30 + 1/42 + 1/56 + .........+1/990

A = 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + ...........+ 1/99.100

A = 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + ....... + 1/99 - 1/100

A = 1/4 - ( -1/5 + 1/5 ) - ( -1/6 + 1/6 ) - ( -1/7 + 1/7 ) - ...........- ( - 1/99 + 1/99 ) - 1/100

A = 1/4 - 0 - 0 - 0 - ........... - 0 - 1/100

A = 1/4 - 1/100

A = 25/100 - 1/100

A = 24/100

A = 6/25

A=1/4.5+1/5.6+1/6.7+1/7.8+.....+1/...

hê,sai đề rùi

\(A=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{990}\)

   \(=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{30.31}\)

    \(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+....+\frac{1}{30}-\frac{1}{31}\)

      \(=\frac{1}{4}-\frac{1}{31}\)

      \(=\frac{27}{124}\)

\(=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}\\ =\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\\ =\dfrac{1}{2}-\dfrac{1}{8}=\dfrac{3}{8}\)

3/8 

\(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\\ =\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}\\ =\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\\ =\dfrac{1}{3}-\dfrac{1}{9}\\ =\dfrac{2}{9}\)

\(a,\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\)

\(=\dfrac{1}{212}\)

A=1/(4X5)+1/(5X6)+1/(6X7)+1/(7X8)+.....+1/(999X10)

A=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+......+1/999+1/9990-1/10

A=1/4-1/99.9X1/100

A=1/4-1/10

A=6/40

Sửa đề: A=-1/20+(-1/30)+(-1/42)+(-1/56)+(-1/72)+(-1/90)

=-(1/20+1/30+...+1/90)

=-(1/4-1/5+1/5-1/6+...+1/9-1/10)

=-1/4+1/10

=-5/20+2/20=-3/20

\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)

\(\frac{1}{2}-\frac{1}{8}=\frac{4}{8}-\frac{1}{8}=\frac{3}{8}\)

D=\(-\dfrac{1}{4.5}\)+(\(-\dfrac{1}{5.6}\))+(\(-\dfrac{1}{6.7}\))+(\(-\dfrac{1}{7.8}\))+(\(-\dfrac{1}{8.9}\))+(\(-\dfrac{1}{9.10}\))

D=\(-\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\right)\)

D=\(-\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)\)

D=\(-\left(\dfrac{1}{4}-\dfrac{1}{10}\right)\)

D=\(-\dfrac{3}{20}\)