\(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{98.100}\)

\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=\frac{1}{2}.\frac{49}{100}\)

\(=\frac{49}{200}\)

Giúp mk mấy bài nhaEdowa Conan

\(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{98.100}\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\)

\(=\frac{1}{2}-\frac{1}{100}\)

\(=\frac{49}{100}\)

=1-1/3-1/2+1/4+1/3-1/5-1/4+1/6+...+1/97-1/99-1/98+1/100

=1-1/2-1/99-1/98=2327/4851

\(\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+...+\frac{1}{97.99}-\frac{1}{98.100}\)

\(=1-\frac{1}{3}-\frac{1}{2}+\frac{1}{4}+\frac{1}{3}-\frac{1}{5}-\frac{1}{4}+\frac{1}{6}+...+\frac{1}{97}-\frac{1}{99}-\frac{1}{98}+\frac{1}{100}\)

\(=1-\frac{1}{2}-\frac{1}{99}-\frac{1}{98}\)

\(=\frac{2327}{4851}\)

Đặt A=1/1.3 - 1/2.4 +1/3.5 -1/4.6 +.....+1/97.99 -1/98.100

     4A= 4/1.3 -4/2.4 +4/3.5 -4/4.6 +.....+4/97.99 -4/98.100

          =(4/1.3 +4/3.5 +...+4/97.99) - (4/2.4 +4/4.6 +...+4/98.100)

          =(1/1 -1/3+1/3-1/5+...+1/97-1/99)-(1/2 -1/4 -....1/98-1/100)

         =(1/1-1/99)-(1/2-1/100)

         4A=98/99 - 99/100

         A= (98/99-99/100) :4

ngắn gọn nhất nè
1/1.3-1/2.4+1/3.5-1/4.6+...+1/97.99-1/98.100 
= 1- 1/3 - 1/2 + 1/4 + 1/3 - 1/5 - 1/4 + 1/6 + ... + 1/97 - 1/99 - 1/98 + 1/100
= 1 - 1/2 - 1/99 - 1/98
= 2327/4851

\(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...........+\frac{1}{98.100}\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\)

\(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)

cho mình nha!

\(C=\dfrac{4}{1.3}.\dfrac{9}{2.4}.\dfrac{16}{3.5}.\dfrac{25}{4.6}....\dfrac{9801}{9800}=\)

\(=\dfrac{2^2.3^2.4^2.5^2.....99^2}{1.2.3^2.4^2.5^2....98^2.99.100}=\dfrac{2.99}{100}=\dfrac{198}{100}=1,98\)

=1/2 - 1/4 + 1/4 - 1/6 + ... + 1/98 - 1/100

=1/2 - 1/100 = 49/100

1/2 - 1/4 +  1/4 - 1/6 + 1/6 - 1/8 + ... + 1/96 - 1/98 + 1/98 - 1/100

= 1/2 - 1/100 

= 49/100

1/2.4 + 1/4.6 + 1/6.8 + ... + 1/96.98 + 1/98.100

= 1/2 . ( 2/2.4 + 2/4.6 + 2/6.8 + ... + 2/96.98 + 2/98.100 )

= 1/2 . ( 1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + ... + 1/96 - 1/98 + 1/98 - 1/100 )

= 1/2 . ( 1/2 - 1/100 )

= 1/2 . ( 50/100 - 1/100 )

= 49/200

\(D=2.4+4.6+...+98.100\)

\(\Rightarrow6D=2.4.6+4.6.6+...+98.100.6\)

\(=2.4.6+4.6.\left(8-2\right)+...+98.100.\left(102-96\right)\)

\(=2.4.6-2.4.6+4.6.8+...+98.100.102-96.98.100\)

\(=98.100.102\)

\(=999600\)

\(\Rightarrow D=\frac{999600}{6}=166600\)

\(D=2.4+4.6+...+98.100\)

\(6D=2.4.6+4.6.6+...+98.100.6\)

\(=2.4.6+4.6.\left(8-2\right)+...+98.100.\left(102-96\right)\)

\(=2.4.6-2.4.6+4.6.8+...+98.100.102\)

\(=98.100.102\)

\(6D=999600\)

\(D=999600:6\)

\(D=166600\)

     \(D=2\left(1.2+2.3+49.50\right)\)

\(\Leftrightarrow3D=1.2.3+2.3.3+...+49.50.3\)

\(=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+49.50.\left(51-48\right)\)

\(=1.2.3+2.3.4-1.2.3+...+49.50.51-48.49.50\)

\(3D=49.50.51\Rightarrow D=\frac{49.50.51}{3}=41650\)

               Vậy\(D=41650\)