A=\(2.\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+......+\frac{1}{240}\right)\)

A=\(2.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{15.16}\right)\)

A=\(2.\left(\frac{1}{4.}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+.......+\frac{1}{15}-\frac{1}{16}\right)\)

A=\(2.\left(\frac{1}{4}-\frac{1}{16}\right)\)

A=\(2.\left(\frac{4}{16}-\frac{1}{16}\right)\)

\(A=2.\frac{3}{16}\)

\(A=\frac{3}{8}\)

\(Vay\) \(A=\frac{3}{8}\)

=2

Ta co: A = 1/10+ 1/15+1/21+...+1/120 

              = 2/20+2/30+2/42+...+2/240=2/(4*5)+2/(5*6)+.....+2/(15*16)

              = 2*[1/(4*5)+1/(5*6)+...........+ 1/(15*16)]

              = 2* [ 1/4-1/5+1/5-1/6+.........+1/15-1/16]

              = 2*[1/4-1/16]

             = 2*3/16

              = 3/8

Vay A=3/8

nhớ giải chi tiết

\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{1}{105}+\frac{1}{210}\)

 =>   \(\frac{1}{2}A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+.....+\frac{1}{210}+\frac{1}{240}\)

                 \(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+.....+\frac{1}{14.15}+\frac{1}{15.16}\)

                 \(=\frac{1}{2}-\frac{1}{3}+\frac{!}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{16}\)

               \(=\frac{1}{2}-\frac{1}{16}=\frac{7}{16}\)

=>   \(A=\frac{7}{8}\)

\(A=\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+...+\dfrac{1}{120}\)
\(=2\left(\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+...+\dfrac{1}{240}\right)\)
\(=2\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+...+\dfrac{1}{15.16}\right)\)
\(=2\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+...+\dfrac{1}{15}-\dfrac{1}{16}\right)\)
\(=2\left(\dfrac{1}{4}-\dfrac{1}{16}\right)\)
\(=2\cdot\dfrac{3}{16}\)
\(=\dfrac{3}{8}\)
\(A:x=759\)
\(\dfrac{3}{8}:x=759\)
\(\Rightarrow x=\dfrac{3}{8}:759=\dfrac{1}{2024}\)
#AvoidMe

A=2(1/20+1/30+...+1/240)

=2(1/4-1/5+1/5-1/6+...+1/15-1/16)

=2*3/16=3/8

A:x=759

=>x=3/8:759=1/2024

1/2A=1/20+1/30*1/42+...+1/240
1/2A=1/4*5+1/5*6+1/6*7+...+1/15*16
1/2A=1/4-1/5+1/5-1/6+1/6-1/7+...1/15-1/16
1/2A=1/4-1/16=3/16
A=3/16:1/2 A=3/8
Ta có: A: x =759
        3/8: x =759
                x=3/8 : 759 = 1/2024

A = 1/10 + 1/15 + 1/21 + ....+ 1/120

= 2/20 + 2/30 + 2/42 +....+ 2/240

= 2/4x5 + 2/5x6 + 2/6x7 + ...+ 2/15x16

= 2 x ( 1/4x5 + 1/5x6 + 1/6x7 +...+ 1/15x16)

=2 x ( 1/4 - 1/5 + 1/5 - 1/6 +1/6 - 1/7 + .....+ 1/15 - 1/16 )

= 2 x ( 1/4 - 1/16 )

= 2 x ( 4/16 - 1/16 )

= 2 x 3/16

= 6/16

= 3/8

tk nhé

Đợi duyệt nhé 

\(A=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{1}{120}\)

Ta có :

\(\frac{1}{10}< 1\)

\(\frac{1}{15}< 1\)

\(\frac{1}{21}< 1\)

........................

\(\frac{1}{120}< 1\)

\(\Rightarrow\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}< 1\)

\(\Rightarrow A< 1\)( đpcm)

Ta có : A =  \(\frac{1}{10}+\frac{1}{15}+...+\frac{1}{120}\)

= \(\frac{1}{20}\times2+\frac{1}{30}\times2+...+\frac{1}{240}\times2\)

= \(2\times\left(\frac{1}{20}+\frac{1}{30}+...+\frac{1}{240}\right)\)

= \(2\times\left(\frac{1}{4\times5}+\frac{1}{5\times6}+...+\frac{1}{15\times16}\right)\)

= \(2\times\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)

= \(2\times\left(\frac{1}{4}-\frac{1}{16}\right)\)

= \(2\times\frac{3}{16}\)

= \(\frac{3}{8}\)< 1 

=> A < 1 

A < 1 nhe ban

1/10+1/15+1/21+...+1/120

=2*(1/20+1/30+1/42+...+1/240)

=2*(1/4*5+1/5*6+...+1/15*16)

=2*(1/4-1/5+1/5-1/6+...+1/15-1/16)

=2*[(1/4-1/16)+(1/5-1.5)+...+(1/15-1/15)]

=2[(4/16-1/16)+0+...+0]]

=2*3/16=3/8

\(S=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{1}{120}\)

\(S=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+....+\frac{2}{240}\)

\(2S=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+....+\frac{1}{240}\)

\(2S=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+.....+\frac{1}{15.16}\)

\(2S=\left(\frac{1}{4}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{7}\right)+.....+\left(\frac{1}{15}-\frac{1}{16}\right)\)

\(2S=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+....+\frac{1}{15}-\frac{1}{16}\)

\(2S=\frac{1}{4}-\frac{1}{16}\)

\(2S=\frac{3}{16}\)

\(S=\frac{3}{8}\)

= 1 : 10 + 1 : 15 + 1 : 21 + ... + 1 : 120

= 1 : (10 + 15 + 21 + ... + 120)

= 1 : 670 = 1/670