Question

[Yukino Tukinoshita]

a)( 456 x 11 + 912 ) x 37  

              74 x 13                

 B )(36 x 333 - 107 x 111) x 121 

                  333 x 11                  

c )  A=  4/1x3 + 4/3x5 + 4/ 5x7 + .....+ 4/49 x 51 

d)   B = 1/2+1/6 +1/12 +1/20 +1/30 +1/42 +1/56 +1/72 +1/90

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Answer 1

[Nguyễn Thiên Kim]

c)   \(A=\frac{4}{1.3}+\frac{4}{3.5}+\frac{4}{5.7}+...+\frac{4}{49.51}\)  

     \(A=2.\left(\frac{2}{1.3}+\frac{2}{2.5}+\frac{2}{5.7}+...+\frac{2}{49.51}\right)\)

     \(A=2.\left(\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{51-49}{49.51}\right)\)

    \(A=2.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\right)\)

    \(A=2.\left(1-\frac{1}{51}\right)=2.\frac{50}{51}=\frac{100}{51}\)

          Vậy \(A=\frac{100}{51}\)

d)        \(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\)

         \(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)

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

          \(B=1-\frac{1}{10}=\frac{9}{10}\)

                       Vậy      \(B=\frac{9}{10}\)