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Ta có : \(C=\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+......+\frac{2}{41.42}\)
\(C=2\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+.....+\frac{1}{41.42}\right)\)
\(C=2\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{41}-\frac{1}{42}\right)\)
\(C=2\left(\frac{1}{3}-\frac{1}{42}\right)\)
\(C=2.\frac{13}{42}=\frac{13}{21}\)
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 = \(\dfrac{1010}{2021}\)
\(\frac{5}{11x16}+\frac{5}{16x21}+...+\frac{5}{61x66}\)
\(=\frac{5}{11}-\frac{5}{16}+\frac{5}{16}-\frac{5}{21}+...+\frac{5}{61}-\frac{5}{66}\)
\(=\frac{5}{11}-\frac{5}{66}+0+...+0\)
\(=\frac{25}{66}\)
~ Ủng hộ nhé anh chị em ~
\(=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
\(=\frac{1}{11}+\left(\frac{1}{16}-\frac{1}{16}\right)+...+\left(\frac{1}{61}-\frac{1}{61}\right)-\frac{1}{21}\)
\(=\frac{1}{11}-\frac{1}{21}\)
\(=\frac{21}{231}-\frac{11}{231}\)
\(=\frac{10}{231}\)
\(A=\frac{55}{11.16}+\frac{55}{16.21}+\frac{55}{21.26}+......+\frac{55}{36.41}\)
\(=11\left(\frac{5}{11.16}+\frac{5}{16.21}+......+\frac{5}{36.41}\right)\)
\(=11.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+.......+\frac{1}{36}-\frac{1}{41}\right)\)
\(=11.\left(\frac{1}{11}-\frac{1}{41}\right)\)
\(=11.\frac{30}{451}=\frac{30}{41}\)
\(\frac{55}{16.21}\)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= \(\frac{30}{41}\)
\(A=11\left(\frac{5}{11.6}+\frac{5}{16.21}+......+\frac{5}{36.41}\right)\)
\(=11\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+.....+\frac{1}{36}-\frac{1}{41}\right)\)
\(=11\left(\frac{1}{11}-\frac{1}{41}\right)\)
\(=11.\frac{30}{451}=\frac{30}{41}\)
Bài 1 :
A=.........
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
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 \(\frac{18}{115}\)
\(\frac{2}{1x6}+\frac{2}{6x11}+\frac{2}{11x16}+\frac{2}{16x21}+\frac{2}{21x26}\)
= \(\frac{2}{6}+\frac{2}{66}+\frac{2}{176}+\frac{2}{336}+\frac{2}{546}\)
= \(\frac{1}{3}+\frac{1}{33}+\frac{1}{88}+\frac{1}{168}+\frac{1}{273}\)
=\(\frac{5}{13}\)
Mình tự nghĩ đấy .
Chúc bạn học tốt!
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=\(\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)=\(\frac{1}{5}.\frac{5}{66}=\frac{1}{66}\)
\(E=\frac{1}{11x16}+\frac{1}{16x21}+\frac{1}{21x26}+...+\frac{1}{61x66}\)
\(E=\frac{1}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}+\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\right)\)
\(E=\frac{1}{5}\left(\frac{1}{11}-\frac{1}{66}\right)\)
\(E=\frac{1}{5}.\frac{5}{66}\)
\(E=\frac{1}{66}\)