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!!!

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

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

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

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

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

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

a) \(\frac{2}{11x16}+\frac{2}{16x21}+...+\frac{2}{61x66}\)

\(=\frac{2}{5}x\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(=\frac{2}{5}x\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(=\frac{2}{5}x\frac{5}{66}\)

\(=\frac{1}{33}\)

b) \(\frac{2}{5x7}+\frac{4}{7x11}+\frac{3}{11x14}+\frac{4}{14x18}+\frac{5}{18x23}+\frac{7}{23x30}\)

\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{18}+\frac{1}{18}-\frac{1}{23}+\frac{1}{23}-\frac{1}{30}\)

\(=\frac{1}{5}-\frac{1}{30}\)

\(=\frac{1}{6}\)

a, \(\frac{2}{11\times16}+\frac{2}{16\times21}+...+\frac{2}{61\times66}\)

\(=\frac{2}{5}\times\left(\frac{5}{11\times16}+...+\frac{5}{61\times66}\right)\)

\(=\frac{2}{5}\times\left(\frac{1}{11}-\frac{1}{16}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(=\frac{2}{5}\times\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(=\frac{2}{5}\times\frac{5}{66}\)

\(=\frac{1}{33}\)

Vậy giá trị của biểu thức trên là : \(\frac{1}{33}\)

b,\(\frac{2}{5\times7}+\frac{4}{7\times11}+\frac{3}{11\times14}+\frac{4}{14\times18}+\frac{5}{18\times23}\)

\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{18}+\frac{1}{18}-\frac{1}{23}\)

\(=\frac{1}{5}-\frac{1}{23}\)

\(=\frac{18}{115}\)

Vậy giá trị của biểu thức trên là \(\frac{18}{115}\)

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

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

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

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

Bài 1:

 A  = \(\dfrac{1}{1\times3}\) + \(\dfrac{1}{3\times5}\) + \(\dfrac{1}{5\times7}\) +...+ \(\dfrac{1}{2019\times2021}\)

A =   \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{2}{1\times3}\) + \(\dfrac{2}{3\times5}\) + \(\dfrac{2}{5\times7}\)+...+ \(\dfrac{2}{2019\times2021}\))

A = \(\dfrac{1}{2}\) \(\times\)( \(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\)+...+ \(\dfrac{1}{2019}\) - \(\dfrac{1}{2021}\))

A = \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{1}{1}\) - \(\dfrac{1}{2021}\))

A = \(\dfrac{1010}{2021}\)

bạn có sử dụng discord không

\(\frac{55}{16.21}\)chứ nhỉ.

A=\(\frac{55}{11.16}+\frac{55}{16.21}+\frac{55}{21.26}+\frac{55}{26.31}+\frac{55}{31.36}+\frac{55}{36.41}\)

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

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

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

A= \(\frac{30}{41}\)

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

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

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

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

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

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

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

a)        \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\)\(=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+...+\left(\frac{1}{98}-\frac{1}{99}\right)+\left(\frac{1}{99}-\frac{1}{100}\right)\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

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

b)       \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}+\frac{1}{110}\)\(=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}+\frac{1}{10.11}\)

     \(=\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{110}\)

       \(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)

c)   \(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{97.99}\)   \(=\frac{13-11}{11.13}+\frac{15-13}{13.15}+\frac{17-15}{15.17}+...+\frac{99-97}{97.99}\)  

\(=\frac{1}{11}+\frac{1}{13}-\frac{1}{13}+\frac{1}{15}-\frac{1}{15}+\frac{1}{17}...+\frac{1}{97}-\frac{1}{99}\)

\(=\frac{1}{11}-\frac{1}{99}=\frac{8}{99}\)

k biet l

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