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\(\frac{2}{1x6}+\frac{2}{6x11}+\frac{2}{11x16}+\frac{2}{16x21}+\frac{2}{21x26}\)
= \(\frac{2}{6}+\frac{2}{66}+\frac{2}{176}+\frac{2}{336}+\frac{2}{546}\)
= \(\frac{1}{3}+\frac{1}{33}+\frac{1}{88}+\frac{1}{168}+\frac{1}{273}\)
=\(\frac{5}{13}\)
Mình tự nghĩ đấy .
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A = \(\dfrac{25}{1\times6}\) + \(\dfrac{25}{6\times11}\) + \(\dfrac{25}{11\times16}\)+\(\dfrac{25}{16\times21}\)+ \(\dfrac{25}{26\times31}\)
A = 5 \(\times\) ( \(\dfrac{5}{1\times6}\)+\(\dfrac{5}{6\times11}\)+\(\dfrac{5}{11\times16}\)+\(\dfrac{5}{16\times21}\)+\(\dfrac{5}{26\times31}\))
A = 5 \(\times\) ( \(\dfrac{1}{1}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{11}\)+ \(\dfrac{1}{11}\)- \(\dfrac{1}{16}\)+ \(\dfrac{1}{16}\)- \(\dfrac{1}{21}\)+ \(\dfrac{1}{26}\)- \(\dfrac{1}{31}\))
A = 5 \(\times\)( 1 - \(\dfrac{1}{31}\))
A = 5 \(\times\) \(\dfrac{30}{31}\)
A = \(\dfrac{150}{31}\)
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
\(\left(1-\dfrac{1}{4}\right)\times\left(1-\dfrac{1}{9}\right)\times...\times\left(1-\dfrac{1}{576}\right)\times\left(1-\dfrac{1}{625}\right)\)
\(=\dfrac{3}{4}\times\dfrac{8}{9}\times\dfrac{15}{16}\times...\times\dfrac{575}{576}\times\dfrac{624}{625}\)
\(=\left(\dfrac{3}{2}\times2\right)\times\left(\dfrac{8}{3}\times3\right)\times\left(\dfrac{15}{4}\times4\right)...\times\left(\dfrac{575}{24}\times24\right)\times\left(\dfrac{624}{25}\times25\right)\)
\(=\dfrac{1\times3\times2\times4\times3\times5\times...\times23\times25\times24\times26}{2\times3\times4\times...\times25\times2\times3\times4\times...\times25}\)
\(=\dfrac{1\times2\times3\times4\times...\times24\times3\times4\times...\times26}{2\times3\times4\times...\times25\times2\times3\times4\times...\times25}\)
\(=\dfrac{1\times26}{2\times25}=\dfrac{26}{50}=\dfrac{13}{25}=0,52\)
=(1-1/2)(1-1/3)*...*(1-1/25)(1+1/2)(1+1/3)*...*(1+1/25)
=1/2*2/3*...*24/25*3/2*4/3*...*26/25
=1/25*26/2
=26/50=13/25
\(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\)
\(=\dfrac{1}{2}-\dfrac{1}{6}\)
\(=\dfrac{1}{3}\)
\(\dfrac{1}{4}\) : 0,25 - \(\dfrac{1}{8}\) : 0,125 + \(\dfrac{1}{2}\) : 0,5 - 1
= 0,25 x 4 - 0,125 x 8 + 0,5 x 2 - 1
= 1 - 1 + 1 - 1
= 0 + 1 - 1
= 1 - 1
= 0
A = \(\dfrac{1}{4}\) : 0,25 - \(\dfrac{1}{8}\): 0,125 + \(\dfrac{1}{2}\): 0,5 - 1
A = \(\dfrac{1}{4}\) x 4 - \(\dfrac{1}{8}\) x 8 + \(\dfrac{1}{2}\) x 2 - 1
A = 1 - 1 + 1 - 1
A = (1 - 1) + (1 - 1)
A = 0
\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+....+\dfrac{1}{110}\)
\(=\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+....+\dfrac{1}{10\times11}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+....+\dfrac{1}{10}-\dfrac{1}{11}\)
\(=1-\dfrac{1}{11}=\dfrac{10}{11}\)
28,37-23,18-16,82+71,63
=(28,37+71,63)-(23,18+16,82)
=60
B=1/1x6 + 1/6x11 + 1/16x21 + 1/21x26 + 1/26x31
=1-1/6+1/6-1/11+1/11-....-1/31
=1-1/31=30/31
a) A = \(\left(28,37+71,63\right)-\left(23,18+16,82\right)\)
= 100 - 40
= 60
b) \(B=\dfrac{1}{1.6}+\dfrac{1}{6.11}+\dfrac{1}{11.16}+\dfrac{1}{16.21}+\dfrac{1}{21.26}+\dfrac{1}{26.31}\)
= \(\dfrac{1}{5}\left(\dfrac{5}{1.6}+\dfrac{5}{6.11}+...+\dfrac{5}{26.31}\right)\)
= \(\dfrac{1}{5}\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{31}\right)\)
= \(\dfrac{1}{5}\left(1-\dfrac{1}{31}\right)=\dfrac{1}{5}.\dfrac{30}{31}=\dfrac{6}{31}\)