a) \(A=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)
=> \(A=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)
=> \(A=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)
b) \(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
=> \(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)
=> \(B=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
=> \(B=\frac{1}{1}-\frac{1}{7}=\frac{6}{7}\)
a, A = 5/11x16 + 5/16x21 + 5/21x26 + ... + 5/61x66
= (5/11 - 5/16) + (5/16 - 5/21) + (5/21 - 5/26) + ... + (5/61 - 5/66)
= 5/11 - 5/66 ( phá ngoặc rồi nhóm biểu thức trên)
= 25/66
b, B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42
= 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7
= (1/1 - 1/2) + (1/2-1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ( 1/5 -1/6) + (1/6 - 1/7)
= 1/1 - 1/7 = 6/7
c, C = 7/3x4x5 + 7/4x5x6 + 7/5x6x7 +... + 7/19x20x21
C =7/2 x ( 2/3x4x5 + 2/4x5x6 + ... + 2/19x20x21)
C = 7/2 x [(1/3-1/4-1/5) + (1/4-1/5-1/6) + ...+(1/19-1/20-1/21)]
C = 7/2 x (1/3 - 1/21) (cũng phá ngoặc rồi nhóm như các câu trên)
C = 1
Dễ nhưng dài quá !
