Đáp án:
`a,``2/3 + 1/3 . ( -4/9 + 5/6 ) : 7/12`
`= 2/3 + 2/9`
`= 8/9`
`b,``2/5 + 3/5 : (3/5 + -2/3)- 3(1)/2`
`= 2/5 + (-9) - 7/2`
`= -121/10`
`c,``(14-8(5)/12) : 3 + 7/36 - (-1/2)^2`
`= 67/36 + 7/36 - 1/4`
`= 65/36`
`1) 5/9 . 7/13 + 5/9 . 9/13 - 5/9 . 3/13`
`= 5/9 . ( 7/13 + 9/13 - 3/13)`
`= 5/9 . 1`
`= 5/9`
`3) -3/5 . 5/7 + -3/5 . 3/7 + -3/5 . 6/7 `
`= -3/5 . ( 5/7 + 3/7 + 6/7)`
`= -3/5 . 2`
`= -6/5`
`4, 1/18 + 1/54 + 1/108 + 1/990`
`= 1/(3.6) + 1/(6.9) + 1/(9.12) + 1/( 12 . 15 )`
`= 1/3 . ( 3/(3.6) + 3/(6.9) + 3/(9.12) + 3/( 12 . 15 ))`
`= 1/3 . ( 1/3 - 1/6 + 1/6 - 1/9 + 1/9 - 1/12 + 1/12 - 1/15)`
`= 1/3 . ( 1/3-1/15)`
`= 1/3 . 4/15`
`=4/45`
`5, 12/(1.4) + 12/(4.7) + 12/(7.10) + 12/(10.13) + ... + 12/(43.46)`
`= 4. ( 3/(1.4)+3/(4.7) + 3/(7.10) + 3/(10.13) + ... + 3/(43.46))`
`= 4. ( 1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + ... + 1/43 - 1/46)`
`= 4 . ( 1 - 1/46)`
`= 4. 45/46`
`= 90/23`
`6, 1/2 . 1/2^2 + 1/2^3 + ...+ 1/2^2020`
Gọi biểu thức trên là A, ta có :
`1/2 . A = ( 1. 1/2 + 1/^2 + ... + 1/2019)`
`1/2 . A - A = ( 1. 1/2 + 1/^2 + ... + 1/2019) - ( 1/2 . 1/2^2 + 1/2^3 + ...+ 1/2^2020 )`
`-3/2.A = 1-1/2^2020`
`A = (1-1/2^2020)/(-3/2)`
`7, 14/(2.4) + 14/(4.6) + 14/(6.8) + ... + 14/(2018.2020)`
`= 7. ( 2/(2.4) +2/(4.6) + 2/(6.8) + ... + 2/(2018.2020))`
`= 7. ( 1/2-1/4+1/4-1/8+...+1/2018-1/2020)`
`= 7. ( 1/2 - 1/2020 )`
`= 7. 1009/2020`
`= 7063/2020`
