Gọi A=\(\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+\frac{1}{80}+\frac{1}{120}\)

     \(A=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12}\)

   \(2A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+\frac{2}{10.12}\)

   \(2A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{10}-\frac{1}{12}\)

  \(2A=1-\frac{1}{12}=\frac{11}{12}\)

   \(A=\frac{11}{12}:2=\frac{11}{24}\)

bạn ơi ban giúp mình câu này nhé

aa*ab=aab+ab

gọi số cần tìm là A

A= 1\8+1\24+1\48+1\80+1\120

A=1\2x4 +1\4x6 +1\6x8 +1\8x10 +1\10x12

A=1\2-1\4 +1\4 -1\6 +1\6-1\8 +1\8-1\10 +1\10 -1\12

A= 1\2- 1\12

A= 5\12

\(\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+\frac{1}{80}+\frac{1}{120}\)

\(=\frac{1}{2}(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12})\)

\(=\frac{1}{2}(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+..+\frac{1}{10}-\frac{1}{12})\)

\(=\frac{1}{2}\cdot\left(\frac{1}{2}-\frac{1}{12}\right)=\frac{1}{2}\cdot\frac{5}{12}=\frac{5}{24}\)

\(1200:24-\left(19-x\right)=38\)

\(\Leftrightarrow50-\left(19-x\right)=38\)

\(\Leftrightarrow19-x=50-38\)

\(\Leftrightarrow19-x=12\)

\(\Leftrightarrow x=7\)

\(2-\left[\left(5\frac{5}{24}+x\right)-7\frac{5}{24}\right]=0\)

\(2-\left[\frac{125}{24}+x-\frac{173}{24}\right]=0\)

\(2-\left(\frac{-48}{24}+x\right)=0\)

\(\frac{-48}{24}+x=2-0=2\)

\(\Rightarrow x=4\)

P/s: Có thể tính sai :<

\(A=1+\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{80}+\dfrac{1}{120}\)

\(=1+\dfrac{1}{2\times4}+\dfrac{1}{4\times6}+\dfrac{1}{6\times8}+\dfrac{1}{8\times10}+\dfrac{1}{10\times12}\)

\(=1+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{12}\)

\(=1+\dfrac{1}{2}-\dfrac{1}{12}=\dfrac{17}{12}\)

2/3 + 7/1 = 2/3 + 7 = 2/3 + 21/3 = 23/3

25/48 + 11/24 = 25/48 + 22/48 = 47/48

5/7 + 3/8 = 40/56 + 21/56 = 61/56

15/24 + 12/6 = 5/8 + 2 = 5/8 + 16/8 = 21/8

5/6 + 4/3 = 5/6 + 8/6 = 13/6

3/8 + 7/12 = 9/24 + 14/24 = 23/24

= 23/3

= 47/48

=61/56

=21/8

=13/6

= 23/24

Cảm ơn mn nhìu nhaaaaaa

các bạn giúp mik với ạ

1)

\(\left(a\right)37+397+3997+39997\)

\(=40-3+400-3+4000-3+40000-3\)

\(=\left(40+400+4000+40000\right)-\left(3+3+3+3\right)\)

\(=44440-12=44428\)

\(\left(b\right)298+2998+29998+299998\)

\(=300-2+3000-2+30000-2+300000-2\)

\(=\left(300+3000+30000+300000\right)-\left(2+2+2+2\right)\)

\(=333300-8=333296\)

\(\left(c\right)9+99+999+9999+99999\)

\(=10-1+100-1+1000-1+10000-1+100000-1\)

\(=\left(10+100+1000+10000+100000\right)-\left(1+1+1+1+1\right)\)

\(=111110-5=111105\)

2)
\(\left(a\right)\left(2+4+6+...+2002+2004+2006\right)-\left(1+3+5+...+2001+2003+2005\right)\)

\(=\left(2-1\right)+\left(4-3\right)+\left(6-5\right)+...+\left(2002-2001\right)+\left(2004-2003\right)+\left(2006-2005\right)\)

\(=1+1+1+...+1+1+1\)( 1003 số 1 )

\(=1003\)

\(\left(b\right)88-87+86-85+84-83+...+6-5+4-3+2-1\)

\(=\left(88-87\right)+\left(86-85\right)+\left(84-83\right)+...+\left(6-5\right)+\left(4-3\right)+\left(2-1\right)\)

\(=1+1+1+...+1+1+1\)( 44 số 1 )

\(=44\)

\(\left(c\right)100-98+96-94+92-90+...+12-10+8-6+4-2\)

\(=\left(100-98\right)+\left(96-94\right)+\left(92-90\right)+...+\left(12-10\right)+\left(8-6\right)+\left(4-2\right)\)

\(=2+2+2+...+2+2+2\) ( 25 số 2 )

\(=50\)

3)

\(\left(a\right)360-357+354-351+348-345+...+312-309+306-303+300-297\)

\(=\left(360-357\right)+\left(354-351\right)+\left(348-345\right)+...+\left(312-309\right)+\left(306-303\right)+\)\(\left(300-297\right)\)

\(=3+3+3+3+3+3+3+3+3+3+3=33\)

\(\left(b\right)2006-1-2-3-4-...-47-48-49-50\)

\(=2006-\left(1+2+3+4+...+47+48+49+50\right)\)

\(=2006-\frac{\left(50+1\right)\left[\left(50-1\right)+1\right]}{2}\)

\(=2006-1275=731\)

\(\left(c\right)280-276+272-268+264-260+...+216-212+208-204+200-196\)

\(=\left(280-276\right)+\left(272-268\right)+\left(264-260\right)+...+\left(216-212\right)+\left(208-204\right)+\)\(\left(200-196\right)\)

\(=4+4+4+4+4+4+4+4+4+4+4=44\)

Cảm ơn bạn nha

\(1\frac{5}{24}=\frac{29}{24}\)

A = 1 + 1/2.4 + 1/4.6 + 1/6.8 + 1/8.10 + 1/10.12

2A = 2 + 2/2.4 + 2/4.6 + 2/6.8 + 2/8.10 + 2/10.12

     = 2 + 1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + 1/8 - 1/10 + 1/10 - 1/12

     = 2 + 1/2 - 1/12 = 29/12

=> A = 29/12 : 2 = 29/24

Tk mk nha

A =1+ 1/2.4 + 1/4.6 +1/6.8+1/8.10+1/10.12

=1+1/2 -1/4 +1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12

=1+1/2-1/12

=3/2-1/12

=17/12

\(\frac{1}{4}+\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+\frac{1}{80}+\frac{1}{120}+\frac{1}{168}\)

\(=\frac{1}{4}.\left(1+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)

\(=\frac{1}{4}.\left(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)

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

\(=\frac{1}{4}.\left(1+1-\frac{1}{7}\right)\)

\(=\frac{1}{4}.\left(2-\frac{1}{7}\right)\)

\(=\frac{1}{4}.\frac{13}{7}=\frac{13}{28}\)

Là 1 phần 4 + 1phan 8+ va cu nhu the