\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....+\frac{1}{x\left(x+1\right):2}=\frac{2001}{2003}\)

\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{x\left(x+1\right)}=\frac{2001}{2003}\)

\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{x\left(x+1\right)}\right)=\frac{2001}{2003}\)

\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{x}-\frac{1}{x+1}=\frac{2001}{2003}:2=\frac{2001}{4006}\)

\(\frac{1}{2}-\frac{1}{x+1}=\frac{2001}{4006}\)

\(\frac{1}{x+1}=\frac{1}{2}-\frac{2001}{4006}=\frac{1}{2003}\)

=> x+1 = 2003

=> x = 2003 - 1

=> x = 2002

thank you very much

a =143

b = 2510

c 28 x 73 = 2044

cái câu c tính nhẩm chết liền

d [ 1700 - 340 +17 ] : 17 = 81

2 . Tìm x 

a 7 . [ x - 3 ] - 6 = 1

   7 . [ x - 3 ]   = 1+6

7 . [ x - 3 ]     = 7

     x - 3 = 7 : 7

x - 3 =1

x=3+1=4

b 

[x+5] .2:11=6

[x+5] x 2  = 6 x 11

[ x + 5 ] x 2 = 66

x+2=66:2

x+2=33

x=33-2=31

Bài 1 

a, \(45+98=143\)

b, \(2605-95=2510\)

c,\(28.73+28\)

\(=28.\left(73+1\right)\)

\(=28.74\)

\(=2072\)

d,\(\left[1700-340+17\right]:17\)

\(=1700:17-340:17+17:17\)

\(=100-20+1\)

\(=81\)

Bài 2 

a, \(7.\left(x-3\right)-6=1\)

\(\Leftrightarrow7.\left(x-3\right)=7\)

\(\Leftrightarrow x-3=1\)

\(\Leftrightarrow x=4\)

b, \(\left(x+2\right).2:11=6\)

\(\Leftrightarrow\left(x+2\right).2=66\)

\(\Leftrightarrow x+2=33\)

\(\Leftrightarrow x=31\)

• a,  Do \(\left[3x-15\right]^7=0\)

                     =>    \(3x-15=0\) 

                     =>    \(3x=0+15\)

                     =>    \(3x=15\)

                     =>    \(x=15:3\)

                     =>    \(x=5\)

\(\left(3x-5\right)^7=0\)

\(\Rightarrow3x-5=0\)

\(\Rightarrow3x=5\)

\(\Rightarrow x=\frac{5}{3}\)

1) \(A=\frac{7}{10\times11}+\frac{7}{11\times12}+\frac{7}{12\times13}+...+\frac{7}{69\times70}\)

    \(A=7\times\left(\frac{1}{10\times11}+\frac{1}{11\times12}+\frac{1}{12\times13}+...+\frac{1}{69\times70}\right)\)

    \(A=7\times\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{69}-\frac{1}{70}\right)\)

    \(A=7\times\left(\frac{1}{10}-\frac{1}{70}\right)\)

   \(A=7\times\frac{3}{35}\)

   \(A=\frac{3}{5}\)

2) \(B=\frac{1}{25\times27}+\frac{1}{27\times29}+\frac{1}{29\times31}+...+\frac{1}{73\times75}\)

    \(B=\frac{1}{2}\times\left(\frac{2}{25\times27}+\frac{2}{27\times29}+\frac{2}{29\times31}+...+\frac{2}{73\times75}\right)\).

    \(B=\frac{1}{2}\times\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)

    \(B=\frac{1}{2}\times\left(\frac{1}{25}-\frac{1}{75}\right)\)

    \(B=\frac{1}{2}\times\frac{2}{75}\)

    \(B=\frac{1}{75}\)

3) \(C=\frac{4}{2\times4}+\frac{4}{4\times6}+\frac{4}{6\times8}+...+\frac{4}{2008\times2010}\)

    \(C=\frac{4}{2}\times\left(\frac{2}{2\times4}+\frac{2}{4\times6}+\frac{2}{6\times8}+...+\frac{2}{2008\times2010}\right)\)

    \(C=2\times\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)

    \(C=2\times\left(\frac{1}{2}-\frac{1}{2010}\right)\)

    \(C=2\times\frac{502}{1005}\)

    \(C=\frac{1004}{1005}\)

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