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\(=11\left(\dfrac{5}{6\cdot11}+\dfrac{5}{11\cdot16}+\dfrac{5}{16\cdot21}+\dfrac{5}{21\cdot26}+\dfrac{5}{26\cdot31}\right)\)
=11(1/6-1/11+1/11-1/16+1/16-1/21+1/21-1/26+1/26-1/31)
=11*25/186=275/186
\(\dfrac{55}{6x11}+\dfrac{55}{11x16}+\dfrac{55}{21x16}+\dfrac{55}{21x26}+\dfrac{55}{31x26}\)
\(=55\left(\dfrac{1}{6x11}+\dfrac{1}{11x16}+\dfrac{1}{21x16}+\dfrac{1}{21x26}+\dfrac{1}{31x26}\right)\)
\(=55\left(\dfrac{1}{5}x\left(\dfrac{1}{6}-\dfrac{1}{11}\right)+\dfrac{1}{5}x\left(\dfrac{1}{11}-\dfrac{1}{16}\right)+\dfrac{1}{5}x\left(\dfrac{1}{16}-\dfrac{1}{21}\right)+\dfrac{1}{5}x\left(\dfrac{1}{21}-\dfrac{1}{26}\right)+\dfrac{1}{5}x\left(\dfrac{1}{26}-\dfrac{1}{31}\right)\right)\)
\(=55x\dfrac{1}{5}x\left(\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{31}\right)\)
\(=11x\left(\dfrac{1}{6}-\dfrac{1}{31}\right)=11x\left(\dfrac{31-6}{186}\right)=11x\dfrac{25}{186}=\dfrac{275}{186}\)
C=\(\dfrac{55}{6\cdot11}\)+\(\dfrac{55}{11\cdot16}\)+\(\dfrac{55}{16\cdot21}\)+\(\dfrac{55}{21\cdot26}\)+\(\dfrac{55}{26\cdot31}\)
=\(\dfrac{1}{6}\)-\(\dfrac{1}{11}\)+\(\dfrac{1}{11}\)-\(\dfrac{1}{16}\)+\(\dfrac{1}{16}\)-\(\dfrac{1}{21}\)+\(\dfrac{1}{21}\)-\(\dfrac{1}{26}\)+\(\dfrac{1}{26}\)-\(\dfrac{1}{31}\)
=\(\dfrac{1}{6}\)-\(\dfrac{1}{31}\)=\(\dfrac{25}{186}\)
\(\frac{2}{1x6}+\frac{2}{6x11}+\frac{2}{11x16}+\frac{2}{16x21}+\frac{2}{21x26}\)
= \(\frac{2}{6}+\frac{2}{66}+\frac{2}{176}+\frac{2}{336}+\frac{2}{546}\)
= \(\frac{1}{3}+\frac{1}{33}+\frac{1}{88}+\frac{1}{168}+\frac{1}{273}\)
=\(\frac{5}{13}\)
Mình tự nghĩ đấy .
Chúc bạn học tốt!
Ta có:
55/11x16+55/16x21+55/21x26x.....x55/36x41
=55/5 x (1/11-1/16+1/16-1/21+.......+1/36-1/41)
=55/5 x (1/11-1/41)
=55/5x30/451
=30/41
nhớ ****
`A = 55/( 11xx16 ) + 55/( 16xx21 ) + 55/( 21xx26 ) + 55/( 26xx31) + 55/( 31xx36)+55/(36xx41)`
`A = 11 xx ( 5/( 11xx16 ) + 5/( 16xx21 ) + 5/( 21xx26 ) + 5/( 26xx31) + 5/( 31xx36)+5/(36xx41)`
`A = 11 xx ( 1/11 - 1/16 + 1/16 - 1/21 + 1/21 - 1/26 + 1/26 - 1/31 + 1/31 - 1/36 + 1/36 - 1/41 )`
`A = 11 xx ( 1/11 - 1/41 )`
`A = 1 - 11/41`
`A = 30/41`
\(A=55.\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{31}+\dfrac{1}{31}-\dfrac{1}{36}+\dfrac{1}{36}-\dfrac{1}{41}\right)\)
\(A=55\times\left(\dfrac{1}{11}-\dfrac{1}{41}\right)=55\times\dfrac{30}{451}=\dfrac{150}{41}\)
\(A=\frac{55}{11x16}+\frac{55}{16x21}+\frac{55}{21x26}+\frac{55}{26x31}+\frac{55}{31x36}+\frac{55}{36x41}\)
\(A=11\left(\frac{5}{11x16}+\frac{5}{16x21}+\frac{5}{21x26}+\frac{5}{26x31}+\frac{5}{31x36}+\frac{5}{36x41}\right)\)
\(A=11\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+\frac{1}{26}-\frac{1}{31}+\frac{1}{31}-\frac{1}{36}+\frac{1}{36}-\frac{1}{41}\right)\)
\(A=11\left(\frac{1}{11}-\frac{1}{41}\right)=1-\frac{11}{41}=\frac{30}{41}\)
\(\frac{55}{11\times6}+\frac{55}{16\times21}+\frac{55}{21\times26}+..+\frac{55}{36\times41}\)
\(=\frac{11-6}{11\times6}+\frac{21-16}{16\times21}+..+\frac{41-36}{36\times41}\)
\(=1-\frac{1}{11}+\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+..+\frac{1}{36}-\frac{1}{41}\)
\(=1-\frac{1}{41}\)
\(=\frac{40}{41}\)
\(A=\frac{55}{11.16}+\frac{55}{16.21}+\frac{55}{21.26}+......+\frac{55}{36.41}\)
\(=11\left(\frac{5}{11.16}+\frac{5}{16.21}+......+\frac{5}{36.41}\right)\)
\(=11.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+.......+\frac{1}{36}-\frac{1}{41}\right)\)
\(=11.\left(\frac{1}{11}-\frac{1}{41}\right)\)
\(=11.\frac{30}{451}=\frac{30}{41}\)
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) \(B=\dfrac{1}{1.6}+\dfrac{1}{6.11}+\dfrac{1}{11.16}+\dfrac{1}{16.21}+\dfrac{1}{21.26}+\dfrac{1}{26.31}\)
= \(\dfrac{1}{5}\left(\dfrac{5}{1.6}+\dfrac{5}{6.11}+...+\dfrac{5}{26.31}\right)\)
= \(\dfrac{1}{5}\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{31}\right)\)
= \(\dfrac{1}{5}\left(1-\dfrac{1}{31}\right)=\dfrac{1}{5}.\dfrac{30}{31}=\dfrac{6}{31}\)
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 = \(\dfrac{150}{31}\)
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