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

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

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

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

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

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

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

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

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

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

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

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

Vậy \(A=\frac{1}{22}\)

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

\(A:3.5=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)

\(A:3.5=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)

\(A:3.5=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)

=> \(A=\frac{5}{66}:5.3=\frac{1}{22}\)

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

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

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

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

\(A=\frac{15}{330}\)

Rồi nha

Ý cha, nếu bạn An Hòa ra = \(\frac{1}{22}\) thì kết quả cuối cùng của bài mình bạn rút gọn đi nha (\(\frac{15}{330}=\frac{1}{22}\))

a) Ta có: \(4\cdot\left(13-16\right)-\left(3-5\right)\cdot\left(-3\right)^2\)

\(=4\cdot13-4\cdot16+2\cdot9\)

\(=52-64+18\)

=6

b) Ta có: \(-\dfrac{2}{5}+\dfrac{7}{11}+\dfrac{-11}{10}+\dfrac{7}{-11}\)

\(=-\left(\dfrac{2}{5}+\dfrac{11}{10}\right)+\left(\dfrac{7}{11}-\dfrac{7}{11}\right)\)

\(=-\left(\dfrac{4}{10}+\dfrac{11}{10}\right)\)

\(=\dfrac{-15}{10}=\dfrac{-3}{2}\)

mik cũng đang ko biết bài này nè

mình cũng thế

1/6+1/12+1/20+...+1/110 = 

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

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

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

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

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:

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

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

...

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

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

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

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

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

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

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

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

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

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

nêu viết đề bài như thế thì nghĩ như là\(\frac{2\cdot4}{1}+\frac{2\cdot7}{4}...\)
=> hai bạn kia sai

Ta có :      3/ 1 x 6 + 3/6 x 11 + 3/11 x 16 + ...+ 3/96 x 101 

= 3/5 x (  5/1 x 6 + 5/6 x 11 + 5/11 x 16 + ...+ 5/96 x 101 ) 

= 3/5 x  (  1 - 1/6 + 1/6 - 1/11 + 1/11 - 1/16 + ...+ 1/96 - 1/101 ) 

= 3/5 x  (  1 - 1/101 ) 

= 3/5 x    100/101 

= 60/101 

Tham khảo nha !!! 

\(1+2+3+...+n=\frac{n\left(n+1\right)}{2}\)

\(1+3+5+7+...+\left(2n-1\right)=n^2\)

\(2+4+6+8+...+2n=n\left(n+1\right)\)