Tính nhanh:
A= $\frac{1}{3}$ + $\frac{1}{150}$ + $\frac{1}{15}$ + $\frac{1}{300}$ + $\frac{1}{35}$ + $\frac{1}
{500}$ + $\frac{1}{63}$ + $\frac{1}{750}$ + $\frac{1}{99}$ + $\frac{1}{1050}$
Tính nhanh:
A= $\frac{1}{3}$ + $\frac{1}{150}$ + $\frac{1}{15}$ + $\frac{1}{300}$ + $\frac{1}{35}$ + $\frac{1}
{500}$ + $\frac{1}{63}$ + $\frac{1}{750}$ + $\frac{1}{99}$ + $\frac{1}{1050}$
Đáp án: `A = 361/770`
Giải thích các bước giải:
`A = 1/3 + 1/150 + 1/15 + 1/300 + 1/35 + 1/500 + 1/63 + 1/750 + 1/99 + 1/1050`
`= (1/3 + 1/15 + 1/35 + 1/63 + 1/99) + (1/150 + 1/300 + 1/500 + 1/750 + 1/1050)`
`= ( 1/(1.3) + 1/(3.5) + 1/(5.7) + 1/(7.9) + 1/(9.11) ) + ( 1/(10.15) + 1/(15.20) + 1/(20.25) + 1/(25.30) + 1/(30.35)`
`= 1/2 . (1 – 1/3 + 1/3 – 1/5 + 1/5 – 1/7 + 1/7 – 1/9 + 1/9 – 1/11) + 1/5 . (1/10 – 1/15 + 1/15 – 1/20 + 1/20 – 1/25 + 1/25 – 1/30 + 1/30 – 1/35)`
`= 1/2 . (1 – 1/11) + 1/5 . (1/10 – 1/35)`
`= 1/2 . 10/11 + 1/5 . 1/14`
`= 5/11 + 1/70`
`= 350/770 + 11/770`
`= 361/770`
Ta có:
A= 1/3+ 1/150+ 1/15+ 1/300+ 1/35+ 1/500+ 1/63+ 1/750+ 1/99+ 1/1050
= ( 1/3+ 1/15+ 1/35+ 1/63+ 1/99)+ ( 1/150+ 1/300+ 1/500+ 1/750+ 1/1050)
= 1/2. ( 2/1.3+ 2/3.5+…+ 2/9.11)+ 1/5. ( 5/10.15+ 5/15.20+ 5/20. 25+ 5/25.30+ 5/30. 35)
= 1/2. ( 1- 1/3+ 1/3- 1/5+ 1/5- 1/7+ 1/7- 1/9+ 1/9- 1/11) + 1/5 . ( 1/10- 1/15+ 1/15- 1/20+ 1/20- 1/25+ 1/25- 1/30+ 1/30- 1/35)
= 1/2. ( 1- 1/11) + 1/5.( 1/10- 1/35)
= 1/2. 10/11+ 1/5. 5/70
= 5/11+ 1/70
= 350/ 770 + 11/770
= 361/770
Chúc bạn học tốt!