\(A=11\left(\frac{5}{11.6}+\frac{5}{16.21}+......+\frac{5}{36.41}\right)\)

\(=11\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+.....+\frac{1}{36}-\frac{1}{41}\right)\)

\(=11\left(\frac{1}{11}-\frac{1}{41}\right)\)

\(=11.\frac{30}{451}=\frac{30}{41}\)

\(S=\frac{5^2}{1\cdot6}+\frac{5^2}{6\cdot11}+\frac{5^2}{11\cdot16}+\frac{5^2}{16\cdot21}+\frac{5^2}{21\cdot26}\)

\(S=\frac{25}{1\cdot6}+\frac{25}{6\cdot11}+\frac{25}{11\cdot16}+\frac{25}{16\cdot21}+\frac{25}{21\cdot26}\)

\(S=5\left[\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+\frac{5}{16\cdot21}+\frac{5}{21\cdot26}\right]\)

\(S=5\left[1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{21}-\frac{1}{26}\right]\)

\(S=5\left[1-\frac{1}{26}\right]=5\cdot\frac{25}{26}=\frac{125}{26}\)

Bài làm

S = \(\frac{5^2}{1.6}\)+ \(\frac{5^2}{6.11}\)+ \(\frac{5^2}{11.16}\)+ \(\frac{5^2}{16.21}\)+\(\frac{5^2}{21.26}\)

S : 5 = \(\frac{5}{1.6}\)+ \(\frac{5}{6.11}\)+ \(\frac{5}{11.16}\) + \(\frac{5}{16.21}\) + \(\frac{5}{21.26}\)

S : 5 = 1 - \(\frac{1}{6}\)+ \(\frac{1}{6}\)- \(\frac{1}{11}\) + \(\frac{1}{11}\)- \(\frac{1}{16}\)+ \(\frac{1}{16}\)- \(\frac{1}{21}\)+ \(\frac{1}{21}\)- \(\frac{1}{26}\)

S : 5 = 1 - \(\frac{1}{26}\)

S : 5 = \(\frac{25}{26}\)

S = \(\frac{125}{26}\)

\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}\)

\(S=5.\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}\right)\)

\(S=5\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}\right)\)

\(S=5\left(1-\frac{1}{26}\right)\)

\(S=5.\frac{25}{26}\)

=>\(S=\frac{125}{26}\)

\(C=\frac{1}{11\cdot16}+\frac{1}{16\cdot21}+...+\frac{1}{61\cdot66}=\frac{5}{5}\cdot\left(\frac{1}{11\cdot16}+\frac{1}{16\cdot21}+...+\frac{1}{61\cdot66}\right)\)

\(=\frac{1}{5}\cdot\left(\frac{5}{11\cdot16}+\frac{5}{16\cdot21}+...+\frac{5}{61\cdot66}\right)=\frac{1}{5}\cdot\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(=\frac{1}{5}\cdot\left[\left(\frac{1}{11}-\frac{1}{66}\right)+\left(\frac{1}{16}-\frac{1}{16}\right)+...+\left(\frac{1}{61}-\frac{1}{61}\right)\right]\)

\(=\frac{1}{5}\cdot\left[\left(\frac{6}{66}-\frac{1}{66}\right)+0+...+0\right]=\frac{1}{5}\cdot\frac{5}{66}=\frac{1\cdot5}{5\cdot66}=\frac{1\cdot1}{1\cdot66}=\frac{1}{66}\)

Vậy \(C=\frac{1}{66}\)

Chúc bạn học tốt!^_^

Ta có : \(C=\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+......+\frac{2}{41.42}\)

\(C=2\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+.....+\frac{1}{41.42}\right)\)

\(C=2\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{41}-\frac{1}{42}\right)\)

\(C=2\left(\frac{1}{3}-\frac{1}{42}\right)\)

\(C=2.\frac{13}{42}=\frac{13}{21}\)

Các bạn chỉ cần trả lời câu C thôi nha!!!

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

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

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

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

E=\(\frac{1}{5}\).(\(\frac{1}{11}-\frac{1}{16}\)+\(\frac{1}{16}-\frac{1}{21}+\frac{1}{21}+\frac{1}{26}+....+\frac{1}{61}-\frac{1}{66}\))

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

\(E=\frac{1}{11x16}+\frac{1}{16x21}+\frac{1}{21x26}+...+\frac{1}{61x66}\)

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

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

\(E=\frac{1}{5}.\frac{5}{66}\)

\(E=\frac{1}{66}\)

\(x-\frac{1}{3}=\frac{9}{20}\)

\(x=\frac{9}{20}+\frac{1}{3}\)

\(x=\frac{9\times3+1\times20}{60}\)

\(x=\frac{47}{60}\)

47/60

\(x-\frac{1}{3}=\frac{9}{20}\)

\(x=\frac{9}{20}+\frac{1}{3}\)

\(x=\frac{47}{60}\)

~ Học Tốt ~

\(\frac{8}{9}\)

\(M=\frac{8}{9}\)

đúng đấy bạn 

\(A=\frac{55}{11.16}+\frac{55}{16.21}+\frac{55}{21.26}+......+\frac{55}{36.41}\)

\(=11\left(\frac{5}{11.16}+\frac{5}{16.21}+......+\frac{5}{36.41}\right)\)

\(=11.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+.......+\frac{1}{36}-\frac{1}{41}\right)\)

\(=11.\left(\frac{1}{11}-\frac{1}{41}\right)\)

\(=11.\frac{30}{451}=\frac{30}{41}\)

toán 5 | Diễn đàn HOCMAI - Cộng đồng học tập lớn nhất Việt Nam

\(A=\frac{55}{11X16}+\frac{55}{16X21}+\frac{55}{21X26}+\frac{55}{26X31}+\frac{55}{31X36}+\frac{55}{36X41}\)

\(A=11X\left(\frac{5}{11X16}+\frac{5}{16X21}+\frac{5}{21X26}+\frac{5}{26X31}+\frac{5}{31X36}+\frac{5}{36X41}\right)\)

\(A=11X\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+\frac{1}{26}-\frac{1}{31}+\frac{1}{31}-\frac{1}{36}+\frac{1}{36}-\frac{1}{41}\right)\)

\(A=11X\left(\frac{1}{11}-\frac{1}{41}\right)\)

\(A=11X\frac{1}{11}-11X\frac{1}{41}\)

\(A=1-\frac{11}{41}\)

\(A=\frac{30}{41}\)

Bài 1 :

A=.........

A=\(11\left(\frac{5}{11\times16}+\frac{5}{16\times21}+...+\frac{5}{36\times41}\right)\)\(+1\frac{11}{41}\)

A=\(11\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-..-\frac{1}{41}\right)\)\(+1\frac{11}{41}\)

A=\(11\left(\frac{1}{11}-\frac{1}{41}\right)+1\frac{11}{41}\)

A=\(\frac{30}{41}+1\frac{11}{41}\)

A=2

Bài 2 :

Đầu con cá nặng là:

\(150+150\times\frac{1}{2}=225\left(g\right)\)

Thân con cá nặng là:

150+225=375 (g)

Vậy con cá nặng là :

150+225+375=750 (g)

Bài 1: \(A=\frac{55}{11\times16}+\frac{55}{16\times21}+...+\frac{55}{36\times41}+1\frac{11}{41}\)

           \(A=\frac{55}{11\times16}+\frac{55}{16\times21}+...+\frac{55}{36\times41}+\frac{52}{41}\)

           \(A=11\times\left(\frac{5}{11\times16}+...+\frac{5}{36\times41}\right)+\frac{52}{41}\)

           \(A=11\times\left(\frac{1}{11}-\frac{1}{16}+...+\frac{1}{36}-\frac{1}{41}\right)+\frac{52}{41}\)

           \(A=11\times\left(\frac{1}{11}-\frac{1}{41}\right)+\frac{52}{41}\) 

           \(A=11\times\left(\frac{41}{451}-\frac{11}{451}\right)+\frac{52}{41}\)

          \(A=11\times\frac{30}{451}+\frac{52}{41}=\frac{30}{41}+\frac{52}{41}=\frac{82}{41}=2\)

Bài 2: Ta thấy: Đầu = Đuôi + \(\frac{1}{2}\)Thân

                        Thân = Đuôi + Đầu

=> Thân = Đuôi + (Đuôi + \(\frac{1}{2}\)Thân) = 2 x Đuôi + \(\frac{1}{2}\)Thân

=> \(\frac{1}{2}\)Thân = 2 x Đuôi = 2 x 150 = 300 (g)

Thân nặng số g là:     300 x 2 = 600 (g)

Đầu nặng số g là:     600 - 150 = 450 (g)

Cân nặng của con cá là:     600 + 450 + 150 = 1200 (g)

            Đáp số: 1200 g