Giúppppp mình vs ạ Cảm ơnnnn mn đã giúp đỡ

thanhnha1151

2 năm trước

Loga Sinh Học lớp 12

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linhhoang1931

`a)A=2+2^3+....+2^19`

`=>2^2A=2^3+2^5+.....+2^21`

`=>4A-A=3A=2^21-2`

`=>A=(2^21-2)/3`

`b)B=1/3+1/3^2+...+1/3^19`

`=>3B=1+1/3+....+1/3^18`

`=>3B-B=2B=1-1/3^19`

`=>B=(1-1/3^19)/2`

`c)C=1/(1.3)+1/(3.5)+....+1/(17.19)`

`=>2C=2/(1.3)+2/(3.5)+.....+2/(17.19)`

`=>2C=1-1/3+1/3-1/5+....+1/17-1/19`

`=>2C=1-1/19=18/19`

`=>C=9/19`

`d)D=1/(1.2.3)+1/(2.3.4)+....+1/(18.19.20)`

`=>2D=2/(1.2.3)+2/(2.3.4)+....+2/(18.19.20)`

`=>2D=1/(1.2)-1/(2.3)+1/(2.3)-1/(3.4)+....+1/(18.19)-1/(19.20)`

`=>2D=1/2-1/380=189/380`

`=>D=189/760`

`e)E=1.2+2.3+3.4+.....+19.20`

`=>3E=1.2.3+2.3.3+....+19.20.3`

`=>3E=1.2.3+2.3.(4-1)+....+19.20.(21-18)`

`=>3E=1.2.3+2.3.4-1.2.3+.....+19.20.21-18.19.20`

`=>3E=19.20.21`

`=>E=19.7.20`

Vote (0) Phản hồi (0) 2 năm trước

lenhutthongnvt

Đáp án:

Bài 13:

a, `A = 2 + 2^3 + 2^5 + .......... + 2^19`

`2^2 A = 2^3 + 2^5 + .............. + 2^21`

`4A - A = (2^3 + 2^5 + ............. + 2^21) - (2 + 2^3 + 2^5 + .......... + 2^19)`

` = 2^3 + 2^5 + ........... + 2^21 - 2 - 2^3 - 2^5 - ............... - 2^19`

` = (2^3 - 2^3) + (2^5 - 2^5) + ......... + (2^19 - 2^19) + 2^21 - 2`

` 3A = 2^21 - 2`

` A = (2^21 - 2)/3`

b, `B = 1/3 + 1/(3^2) + 1/(3^3) + ........... + 1/(3^19)`

` 3B = 1 + 1/3 + 1/(3^2) + ........... + 1/(3^18)`

` 3B - B = (1 + 1/3 + 1/(3^2) + ........... + 1/(3^18)) - (1/3 + 1/(3^2) + ........... + 1/(3^19))`

` = 1 + 1/3 + 1/(3^2) + ............ + 1/(3^19) - 1/3 - 1/(3^2) - ........... - 1/(3^19)`

` = 1 + (1/3 - 1/3) + (1/(3^2) - 1/(3^2) ) - ................. - (1/(3^18) - 1/(3^18) ) - 1/(3^19)`

` 2B = 1 - 1/(3^19)`

` B = (1 - 1/(3^19) ) /2`

c, `C = 1/(1.3) + 1/(3.5) + ................ + 1/(17.19)`

` = 1/2 . (2/(1.3) + 2/(3.5) + .......... + 2/(17.19) )`

` = 1/2 . (1 - 1/3 + 1/3 - 1/5 + ........ + 1/17 - 1/19)`

` = 1/2 . (1 - (1/3 - 1/3) - (1/5 - 1/5) - ............ - (1/17 - 1/17) - 1/19)`

` = 1/2 . (1 - 1/19)`

` = 1/2 . 18/19`

` = 9/19`

d, `D = 1/(1.2.3) + 1/(2.3.4) + 1/(3.4.5) + .......... + 1/(18.19.20)`

` = 1/2 . (2/(1.2.3) + 2/(2.3.4) + 2/(3.4.5) +.................. + 2/(18.19.20) )`

` = 1/2 . ( 1/(1.2) - 1/(2.3) + 1/(2.3) - 1/(3.4) + ............. + 1/(18.19) - 1/(19.20))`

` = 1/2 . (1/(1.2) -(1/(2.3) - 1/(2.3) ) - (1/(3.4) - 1/(3.4) ) - .......... - (1/(18.19) - 1/(18.19) ) - 1/(19.20))`

` = 1/2 . (1/(1.2) - 1/(19.20))`

` =1/2 . (1/2 - 1/380)`

` = 1/2 . 189/380`

` = 189/760`

e, `E = 1 . 2 + 2 . 3 + 3 . 4 + ............. + 19 . 20`

` E = 1/3 . ( 1 . 2 . 3 + 2 . 3 . 3 + 3 . 4 . 3 + ................ + 19 . 20 . 3)`

` = 1/3 . ( 1 . 2 . 3 + 2 . 3 . (4 - 1) + 3 . 4 . (5 - 2) + .............. + 19 . 20 . (21 - 18) )`

` = 1/3 . ( 1 . 2 . 3 - 1 . 2 . 3 + 2 . 3 . 4 - 2 . 3 . 4 + ............. + 18 . 19 . 20 - 18 . 19 . 20 + 19 . 20 . 21)`

` = 1/3 . ( (1 . 2 . 3 - 1 . 2 . 3) + (2 . 3 . 4 - 2 . 3 . 4) + ......... + (18 . 19 . 20 - 18 . 19 . 20) + 19 . 20 . 21)`

` = 1/3 . ( 19 . 20 . 21)`

` = 19 . 20 . 7`

` = 133 . 20`

` = 2660`

Vote (0) Phản hồi (0) 2 năm trước

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