\(\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}+\frac{2}{11\times13}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\)

\(=\frac{1}{3}-\frac{1}{13}\)

\(=\frac{13}{39}-\frac{3}{39}=\frac{13-3}{39}=\frac{10}{39}\)

10/39

 là hỗn số hả  bn ??

          \(A=11\frac{2}{1.3}+11\frac{2}{3.5}+11\frac{2}{5.7}+11\frac{2}{7.9}+11\frac{2}{9.11}\)

         \(A=11+\frac{2}{1.3}+11+\frac{2}{3.5}+11+\frac{2}{5.7}+11+\frac{2}{7.9}+11+\frac{2}{9.11}\)

         \(A=55+\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)

        \(A=55+\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)

       \(A=55+\frac{1}{1}-\frac{1}{11}\)

      \(A=56-\frac{1}{11}\)

     \(A=\frac{616}{11}-\frac{1}{11}=\frac{615}{11}\)

  Vậy A = 615 / 11 

\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\)

\(=\frac{1}{1}-\frac{1}{11}=\frac{10}{11}\)

10/11

có thể đây là bài lớp 4 nhưng mình nghĩ là các bạn lớp 5 cũng sẽ khó khăn đó

dành cho các bn học sinh giỏi

\(B=\frac{2}{8}+\frac{2}{24}+\frac{2}{48}+...+\frac{2}{18\cdot20}\)

\(B=\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+\frac{2}{6\cdot8}+...+\frac{2}{18\cdot20}\)

\(B=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{18}-\frac{1}{20}\)

\(B=\frac{1}{2}-\frac{1}{20}\)

\(B=\frac{9}{20}\)

=))

\(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\)

\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)

\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(A=\frac{1}{2}+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+...+\left(\frac{1}{9}-\frac{1}{9}\right)-\frac{1}{10}\)

\(A=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}\)

\(2009-\left(4\frac{5}{9}+x-7\frac{7}{18}\right):15\frac{2}{3}=2008\)

\(2009-\left(\frac{41}{9}+x-\frac{133}{8}\right):\frac{47}{3}=2008\)

\(2009-\left(\frac{41}{9}+x-\frac{133}{8}\right)\times\frac{3}{47}=2008\)

\(2009-\frac{41}{9}\times\frac{3}{47}-x\times\frac{3}{47}+\frac{133}{8}\times\frac{3}{47}=2008\)

\(2009-\frac{41}{141}-x\times\frac{3}{47}+\frac{399}{376}=2008\)

\(2009+(\frac{399}{376}-\frac{41}{141})-x\times\frac{3}{47}=2008\)

\((2009+\frac{869}{1128})-x\times\frac{3}{47}=2008\)

\(x\times\frac{3}{47}=2009+\frac{869}{1128}-2008\)

\(x\times\frac{3}{47}=1\frac{869}{1128}\)

\(x\times\frac{3}{47}=\frac{1997}{1128}\)

\(x=\frac{1997}{1128}:\frac{3}{47}\)

\(x=\frac{1997}{72}\)

\(2009-\left(4\frac{5}{9}+x-7\frac{7}{18}\right):15\frac{2}{3}=\)2008

\(\left(\frac{41}{9}+x-\frac{133}{18}\right):\frac{47}{3}=2009-2008\)

\(\left(\frac{41}{9}+x-\frac{133}{18}\right)=1.\frac{47}{3}=\frac{47}{3}\)

\(\frac{82}{18}+x-\frac{133}{18}=\frac{47}{3}\)

\(x=\frac{282}{18}-\frac{82}{18}+\frac{133}{18}\)

\(x=\frac{333}{18}=\frac{37}{2}\)

Đáp số \(x=\frac{37}{2}\)

xin lỗi bn dấu nhân nó bị trùng với x nên mk thay dấu nhân thành dấu "." theo cách lớp 6 nha.

Nếu có chỗ nào sai thì mk xin lỗi các bạn và mong các bạn góp ý 

*****Chúc bạn học giỏi*****

=2/2 - 2/3 - 2/4 - .........- 2/38 - 2/39 - 2/40

= 2/2 - 2/40

=1   - 2/40

=38/40

= 19/20

mk ko hiểu cho lắm bn có thể giải thích rõ hơn ko ? 

1/10+4/20+9/30+16/40+25/50+36/60+49/70+64/80+81/90

=1/10+2/10+3/10+4/10+5/10+6/10+7/10+8/10+9/10

=1+2+3+4+5+6+7+8+9/10

=45/10 (tự rút gọn)

Rút gọn các phân số ta có :

 1/10 + 2/10 + 3/10 + 4/10 + 5/10 + 6/10 + 7/10 + 8/10 + 9/10

= ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 ) / 10 

= 45/10 = 4,5