a/ A=$\frac{1}{5×6}$ +$\frac{1}{6×7}$ +$\frac{1}{7×8}$ +….+ $\frac{1}{200×2001}$
b/ B=$\frac{3}{3×5}$ +$\frac{3}{5×7}$ +$\frac{3}{7×9}$ +….+ $\frac{3}{49×51}$
c/ C=$\frac{5}{1×6}$ +$\frac{5}{6×11}$ +$\frac{5}{11×16}$ +….+ $\frac{5}{26×31}$
a/ A=$\frac{1}{5×6}$ +$\frac{1}{6×7}$ +$\frac{1}{7×8}$ +….+ $\frac{1}{200×2001}$
b/ B=$\frac{3}{3×5}$ +$\frac{3}{5×7}$ +$\frac{3}{7×9}$ +….+ $\frac{3}{49×51}$
c/ C=$\frac{5}{1×6}$ +$\frac{5}{6×11}$ +$\frac{5}{11×16}$ +….+ $\frac{5}{26×31}$
Đáp án:
Giải thích các bước giải:
`A=1/(5.6)+1/(6.7)+1/(7.8)+….+1/(200.201)`
`=1/5-1/6+1/6-1/7+1/7-1/8+….+1/200-1/201`
`=1/5-1/201`
`=196/1005`
`B=3/2[2/(3.5)+2/(5.7)+2/(7.9)+…+2/(49.51)]`
`=3/2(1/3-1/5+15-1/7+1/7-1/9+…+1/49-1/51)`
`=3/2.(16/51)`
`=8/17`
`C=1-1/6+1/6-1/11+1/11-1/16+….+1/26-1/31`
`=1-1/31=30/31`
`a) A = 1/(5 X 6) + 1/(6 X 7) + 1/(7 X 8) + … + 1/(200 X 201)`
`⇒ A = 1/5 – 1/6 + 1/6 – 1/7 + 1/7 – 1/8 + … + 1/200 – 1/201`
`⇒ A = 1/5 – 1/201`
`⇒ A = 201/1005 – 5/1005`
`⇒ A = 196/1005`
Vậy `A = 196/1005`
`b) B = 3/(3 X 5) + 3/(5 X 7) + 3/(7 X 9) + … + 3/(49 X 51)`
`⇒ B = 3/2 . ( 2/(3 X 5) + 2/(5 X 7) + 2/(7 X 9) + … + 2/(49 X 51) )`
`⇒ B = 3/2 . ( 1/3 – 1/5 + 1/5 – 1/7 + 1/7 – 1/9 + … + 1/49 – 1/51 )`
`⇒ B = 3/2 . ( 1/3 – 1/51 )`
`⇒ B = 3/2 . ( 51/153 – 3/153 )`
`⇒ B = 3/2 . 16/51`
`⇒ B = 8/17`
Vậy `B = 8/17`
`c) C = 5/(1 X 6) + 5/(6 X 11) + 5/(11 X 16) + … + 5/(26 X 31)`
`⇒ C = 1/1 – 1/6 + 1/6 – 1/11 + 1/11 – 1/16 + … + 1/26 – 1/31`
`⇒ C = 1/1 – 1/31`
`⇒ C = 31/31 – 1/31`
`⇒ C = 30/31`
Vậy `C = 30/31`