Bài 1: (1đ) Tính: A= $\frac{1}{2}$ + $\frac{5}{6}$ + $\frac{11}{12}$ + $\frac{19}{20}$ + $\frac{20}{30}$ + $\frac{41}{42}$ + $\frac{55}{56}$ + $\frac{71}{72}$ + $\frac{89}{90}$
Bài 2: (4đ) Tính giá trị biểu trị biểu thức:
A = $\frac{2}{1.2.3}$ + $\frac{2}{2.3.4}$ + $\frac{2}{3.4.5}$ + … + $\frac{2}{98.99.100}$
Đáp án: + Giải thích các bước giải:
Bài 1 :
`A = 1/2 + 5/6 + 11/12 + 19/20 + 20/30 + 41/42 + 55/56 + 71/72 + 89/90`
`= 1 – 1/2 + 1 – 1/6 + 1 – 1/12 + 1 – 1/20 + 1 – 1/30 + 1 – 1/42 + 1 – 1/56 + 1 – 1/72 + 1 – 1/90`
`= 9 – (1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90)`
`= 9 – (1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 +1/9.10)`
`= 9 – (1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + 1/5 – 1/6 + 1/6 – 1/7 + 1/7 – 1/8 + 1/8 – 1/9 + 1/9 – 1/10)`
`= 9 – (1 – 1/10)`
`= 9 – 9/10`
`= 81/10`
Bài 2 :
`A = 2/(1.2.3) + 2/(2.3.4) + 2/(3.4.5) + … + 2/(98.99.100)`
`2A = 1/1.2 – 1/2.3 + 1/2.3 – 1/3.4 +…+ 1/98.99 – 1/99.100`
`2A = 1/2 – 1/9900`
`2A = 4949/19800`