TH1) 

\(B=\dfrac{2}{11x15}+\dfrac{2}{15x19}+\dfrac{2}{19x23}+......+\dfrac{2}{51x55}\)

\(B=\dfrac{2}{11}-\dfrac{2}{15}+\dfrac{2}{15}-\dfrac{2}{19}+\dfrac{2}{19}-\dfrac{2}{23}+.....+\dfrac{2}{51}-\dfrac{2}{55}\)

\(B=\dfrac{2}{11}-\dfrac{2}{55}\)

\(B=\dfrac{8}{55}\)

TH2)

\(B=\dfrac{2}{11x15}-\dfrac{2}{15x19}-\dfrac{2}{19x23}-......-\dfrac{2}{51x55}\)

\(B=\dfrac{2}{11}+\dfrac{2}{15}-\dfrac{2}{15}+\dfrac{2}{19}-\dfrac{2}{19}+\dfrac{2}{23}-....-\dfrac{2}{51}+\dfrac{2}{55}\)

\(B=\dfrac{2}{11}+\dfrac{2}{55}\)

\(B=\dfrac{12}{55}\)

15 x 19 : 5 = 15 : 5 x 19

                = 3 x 19

                = 57    

= 15 : 5 x 19

= 3 x 19

= 57

 15 x 19 : 5

= 15 : 5 x 19

= 3 x 19 

= 57

B=2/11x15+2/15x19+2/19x23+...+2/51x55

=>2B=4/11x15+4/15x19+4/19x23+...+4/51x55

=1/11-1/15+1/15-1/19+...+1/51-1/55

=1/11-1/55

=5/55-1/55

=4/55

=>B=4/55 : 2

=4/55.1/2

=2/55

\(B=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+...+\frac{1}{51}-\frac{1}{55}\right)\)

\(B=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{1}{2}.\frac{4}{55}=\frac{2}{55}\)

SỬa đề: \(\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+...+\dfrac{4}{23\cdot27}\)

\(=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{23}-\dfrac{1}{27}\)

=1/3-1/27

=8/27

\(A=\dfrac{4}{3.7}+\dfrac{4}{7.11}+\dfrac{4}{11.15}+\dfrac{4}{15.19}+\dfrac{4}{19.23}+\dfrac{4}{23.27}\)(Dấu . là dấu nhân)
\(=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{15}+\dfrac{1}{15}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{27}\)
\(=\dfrac{1}{3}-\dfrac{1}{27}\)
\(=\dfrac{9}{27}-\dfrac{1}{27}\)
\(=\dfrac{8}{27}\)

A = 4/3x7 + 4/7x11+ 4/11x15 + 4/15x19 + 4/19 x23 + 4/23 x 27

A = 1/3-1/7+1/7-1/11+1/11-1/15+1/15-1/19+1/19-1/23+1/23 -1/27

A = 1/3 - 1/27

A = 8/27

25x14x4

=(25x4)x14

=100x14

=1400

15x19:5

=(15:5)x19

=3x19

=57

31x2x8x5

=(31x8)x(2x5)

=248x10

=2480

25 × 14 × 4 = (25 × 4 ) × 14

                     =100 × 14 

                     = 1 400

15 × 19 : 5 = ( 15 : 5 ) × 19

                    = 3 × 19

                  = 57

31 × 2 × 8 × 5 = (31 × 8 ) × ( 2 × 5 )

                        = 248 × 10

                        = 2 480

25x14x4=25x4x14=100x14=1400

15x19:5=15:5x19=3x19=57

31x2x8x5=2x5x31x8=10x31x8=310x8=2480

\(C=\frac{2}{11.15}+\frac{2}{15.19}+\frac{2}{19.13}+...+\frac{2}{51.55}\)

\(2.C=\frac{4}{11.15}+\frac{4}{15.19}+\frac{4}{19.23}+...+\frac{4}{51.55}\)

\(2.C=\frac{1}{11}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+\frac{1}{19}-\frac{1}{23}+...+\frac{1}{51}-\frac{1}{55}\)

\(2.C=\frac{1}{11}-\frac{1}{55}\)

\(2.C=\frac{5}{55}-\frac{1}{55}=\frac{4}{55}\)

\(C=\frac{4}{55}:2=\frac{4}{55}.\frac{1}{2}=\frac{2}{55}\)

Vậy \(C=\frac{2}{55}\)

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