Cách viết nào sau đây là đúng:
A. /-55/ = -55 B. /-55/ = 55 C. -/-55/ = 55 D. -/55/ = 55
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Ta có: 55 + 55 + 55 + 55 + 55 = 5. 55 = 51. 55 = 56
Chọn (C) 56.
\(=11\left(\dfrac{5}{6\cdot11}+\dfrac{5}{11\cdot16}+\dfrac{5}{16\cdot21}+\dfrac{5}{21\cdot26}+\dfrac{5}{26\cdot31}\right)\)
=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=\(\dfrac{55}{6\cdot11}\)+\(\dfrac{55}{11\cdot16}\)+\(\dfrac{55}{16\cdot21}\)+\(\dfrac{55}{21\cdot26}\)+\(\dfrac{55}{26\cdot31}\)
=\(\dfrac{1}{6}\)-\(\dfrac{1}{11}\)+\(\dfrac{1}{11}\)-\(\dfrac{1}{16}\)+\(\dfrac{1}{16}\)-\(\dfrac{1}{21}\)+\(\dfrac{1}{21}\)-\(\dfrac{1}{26}\)+\(\dfrac{1}{26}\)-\(\dfrac{1}{31}\)
=\(\dfrac{1}{6}\)-\(\dfrac{1}{31}\)=\(\dfrac{25}{186}\)
\(A=11\left(\frac{5}{11.6}+\frac{5}{16.21}+......+\frac{5}{36.41}\right)\)
\(=11\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+.....+\frac{1}{36}-\frac{1}{41}\right)\)
\(=11\left(\frac{1}{11}-\frac{1}{41}\right)\)
\(=11.\frac{30}{451}=\frac{30}{41}\)
B
trừ a,c,d ra :)))