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R = 5 / 11 * 16 + 5 / 16 * 21 + ...+ 5 / 61 * 66

= 1/11 - 1/16 + 1/16 - 1/21 + ... + 1/61 - 1/66

= 1/11 - 1/66

= 5/66

17 tháng 7 2016

\(R=\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\)

\(R=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)

\( R=\frac{1}{11}-\frac{1}{66}=\frac{6}{66}-\frac{1}{66}=\frac{5}{66}\)

9 tháng 8 2016

\(=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)

\(=\frac{1}{11}-\frac{1}{66}=\frac{6}{66}-\frac{1}{66}=\frac{5}{66}\)

9 tháng 8 2016

Thank you

29 tháng 7 2016

a)\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{98.99}+\frac{1}{99.100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}\)

\(=\frac{99}{100}\)

b)\(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\)

\(=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+....+\frac{1}{61}-\frac{1}{66}\)

\(=\frac{1}{11}-\frac{1}{66}\)

\(=\frac{5}{66}\)

29 tháng 7 2016

a,\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\)

ta có:

\(\frac{1}{1.2}=\frac{2-1}{1.2}=\frac{2}{1.2}-\frac{1}{1.2}=1-\frac{1}{2}\)

\(\frac{1}{2.3}=\frac{3-2}{2.3}=\frac{3}{2.3}-\frac{2}{2.3}=\frac{1}{2}-\frac{1}{3}\)

...

\(\frac{1}{99.100}=\frac{1}{99}-\frac{1}{100}\)

= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

=\(1-\frac{1}{100}=\frac{99}{100}\)

b,

\(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.16}+...+\frac{5}{61.66}\)

ta có:

\(\frac{5}{11.16}=\frac{16-11}{11.16}=\frac{16}{11.16}-\frac{11}{11.16}=\frac{1}{11}-\frac{1}{16}\)

\(\frac{5}{16.21}=\frac{21-16}{16.21}=\frac{21}{16.21}-\frac{16}{16.21}=\frac{1}{16}-\frac{1}{21}\)

...

\(\frac{5}{61.66}=\frac{66-61}{61.66}=\frac{66}{61.66}-\frac{61}{61.66}=\frac{1}{61}-\frac{1}{66}\)

= \(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)

=\(\frac{1}{11}-\frac{1}{66}\)=\(\frac{5}{66}\)

10 tháng 1 2016

a. \(C=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)

\(=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)

b. \(D=\frac{2}{3}.\left(\frac{3}{1.4}+\frac{4}{4.7}+...+\frac{3}{97.100}\right)\)

\(=\frac{2}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\right)\)

\(=\frac{2}{3}.\left(1-\frac{1}{100}\right)=\frac{2}{3}.\frac{99}{100}=\frac{33}{50}\)

10 tháng 1 2016

\(C=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-....-\frac{1}{66}\)

\(C=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)

\(D=\frac{2}{3}.\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-....-\frac{1}{100}\right)\)

\(D=\frac{2}{3}.\left(1-\frac{1}{100}\right)=\frac{2}{3}.\frac{99}{100}=\frac{33}{50}\)

15 tháng 7 2017

\(A=\dfrac{5}{11.16}+\dfrac{5}{16.21}+\dfrac{5}{21.26}+...............+\dfrac{5}{61.66}\)

\(\Leftrightarrow A=\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{26}+............+\dfrac{1}{61}-\dfrac{1}{66}\)

\(\Leftrightarrow A=\dfrac{1}{11}-\dfrac{1}{66}=\dfrac{5}{66}\)

15 tháng 7 2017

\(A=\dfrac{5}{11\times16}+\dfrac{5}{16\times21}+\dfrac{5}{21\times26}+...+\dfrac{5}{61\times66}\)

\(=\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{26}+...+\dfrac{1}{61}-\dfrac{1}{66}\)

\(=\dfrac{1}{11}-\dfrac{1}{66}\)

\(=\dfrac{5}{66}\)

~ Học tốt ~

17 tháng 6 2016

a, \(\frac{5}{11.16}+\frac{5}{11.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)

=\(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)

=\(\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)

17 tháng 6 2016

a, A=1/11-1/16+1/16-1/21+1/21-1/26+...+1/61-1/66

      = 1/11-1/66=5/66 ( A chính là biểu thức ở phần a)

b, 1/12+1/20+1/30+...+1/110

=1/3.4+1/4.5+1/5.6+..+1/10.11

=1/3-1/4+1/4-1/5+1/5-1/6+...+1/10-1/11

=1/3-1/11=8/33

25 tháng 7 2016

c)đề sai ở phân số cuối

D ) 1/11×16 +1/16×21+...+1/61×66

Đặt Thắng=1/11×16 +1/16×21+...+1/61×66

5Thắng=5(1/11×16 +1/16×21+...+1/61×66)

5Thắng=1/11-1/16+1/16-1/21+...+1/61-1/66

5Thắng=1/11-1/66

Thắng=5/176:5=1/176

25 tháng 7 2016

D) Đặt D=1/11×16 +1/16×21+...+1/61×66

=>5D=5.(1/11x16+1/16x21+...+1/61x66)

=>5D=5/11x16+5/16x21+...+5/61x66

=>5D=1/11-1/16+1/16-1/21+...+1/61-1/66

=>5D=1/11-1/66

=>5D=5/66

=>D=1/66

29 tháng 9 2016

 A= 3/11*16+3/16*21+3/21*26+.....+3/61*66

\(=\frac{3}{5}\left(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\right)\)

\(=\frac{3}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(=\frac{3}{5}\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(=\frac{3}{5}\cdot\frac{5}{66}\)

\(=\frac{1}{22}\)

29 tháng 9 2016

\(A=\frac{3}{11.16}+\frac{3}{16.21}+\frac{3}{21.26}+...+\frac{3}{61.66}\)

\(\Rightarrow A=\frac{3}{5}\left(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\right)\)

\(\Rightarrow A=\frac{3}{5}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(\Rightarrow A=\frac{3}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(\Rightarrow A=\frac{3}{5}.\frac{5}{66}\)

\(\Rightarrow A=\frac{1}{22}\)

Vậy \(A=\frac{1}{22}\)