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B = 1/4 x( 4/ 1x3x5 +4 /3x5x7 +...+ 4/47x49x51)
= 1/4 x( 1/ 1x3 - 1/3x5 +1/3x5 -1/5x7 +...+ 1/47x49 -1/49x51)
= 1/4 x( 1/1x3 -1/49x51)
= 1/4 x( 1/3 - 1/2499)
= 1/4 x 832/2499
= 208 /2499
Vậy B= 208 /2499
C= 1/ 9x11 -1/ 11x13 +1/ 11x13 -1/ 13x15 +... + 1/ 59x61 -1/61x63
= 1/ 9x11 -1/ 61x63
= 1/99 -1/3843
= 416 /42273
Vậy C= 416 /42273
![](https://rs.olm.vn/images/avt/0.png?1311)
a) $371+731-271-531$
$=(371-271)+(731-531)$
$=100+200$
$=300$
b) $57+58+59+60+61-17-18-19-20-21$
$=(57-17)+(58-18)+(59-19)+(60-20)+(61-21)$
$=40+40+40+40+40$
$=40\cdot5$
$=200$
c) $9-10+11-12+13-14+15-16$
$=(9-10)+(11-12)+(13-14)+(15-16)$
$=-1+(-1)+(-1)+(-1)$
$=-1\cdot4$
$=-4$
$\text{#}Toru$
![](https://rs.olm.vn/images/avt/0.png?1311)
\(C=\frac{4}{9.11.13}+\frac{4}{11.13.15}+...+\frac{4}{59.61.63}\)
\(=2\left(\frac{2}{9.11.13}+\frac{2}{11.13.15}+...+\frac{2}{59.61.63}\right)\)
\(=2\left(\frac{1}{9.11}-\frac{1}{11.13}+\frac{1}{11.13}-\frac{1}{13.15}+...+\frac{1}{59.61}-\frac{1}{61.63}\right)\)
\(=2\left(\frac{1}{9.11}-\frac{1}{61.63}\right)\)
\(=2.\frac{416}{42273}\)
\(=\frac{832}{42273}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) tự làm
b) (57-17)+(58-18)+(59-19)+(60-20)+(61-21)=40+40+40+40+40=200
c) (9+15)+(11+13)+(-10-14)+(-12-12-4)=24+24-24-24-4=-4
d)-(1+2+3+.....+2007)=\(-\dfrac{\left(1+2007\right).2007}{2}=-2015028\)
a) (371-271)+(731-531)=100+200=300
b) (57-17)+(58-18)+(59-19)+(60-20)+(61-21)=40+40+40+40+40=200
c) (9+15)+(11+13)+(-10-14)+(-12-12-4)=24+24-24-24-4=-4
d)-(1+2+3+.....+2007)=−(1+2007).20072=−2015028
![](https://rs.olm.vn/images/avt/0.png?1311)
a. 57 + 58 + 59 + 60 + 61 - 17- 18 - 19 - 20 - 21
= (57 - 17) + (58 - 18) + (59 - 19) + (60 - 20) + (61 - 21)
= 40 + 40 + 40 + 40 + 40
= 40 . 5
= 200
b. 9 - 10 + 11 - 12 + 13 - 14 + 15 - 16
= ( 9 - 10 ) + ( 11 - 12 ) + ( 13 - 14 ) + ( 15 - 16 )
= -1 + (-1) + (-1) + (-1)
= (-1) . 4
= -4
![](https://rs.olm.vn/images/avt/0.png?1311)
Số số hạng:
(61 - 11) : 2 + 1 = 26 (số)
11 + (-13) + 15 + (-17) + ... + 59 + (-61)
= (11 - 13) + (15 - 17) + ... + (59 - 61)
= -2 - 2 - ... - 2 (13 số 2)
= -26
![](https://rs.olm.vn/images/avt/0.png?1311)
a)
\( 49.(51 - 4) - 51.(49 + 4)\)
\(=49.51-49.4-51.49-51.4\)
\(=49.(51-4-51)-51.4\)
\(=49.(-4)-51.4\)
\(=4.(-49-51)\)
\(=4.(-100)\)
\(=-400\)
b)
\( 71.64 + 32.(-7) - 13.32\)
\(=71.32.2+32.(-7)-13.32\)
\(=142.32+32.(-7)-13.32\)
\(=32.(142-7-13)\)
\(=32.122\)
\(=3904\)
c)
\( 11 + (-13) + 15 + (-17) + ... + 59 + (-61)\)
\(=(-2)+(-2)+...+(-2)\)
\(=(-2).13\)
\(=-26\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a. 49.51- 49.4 -51.49 -51.4
= -49.4 - 51.4
=4.(-49-51)
=4.-100
=-400
b.71.64 + 32.(-7) -13.32
= 71.64 + 32.(-7-13)
=71.64 + 32.-20
=71.32.2 +32.-20
=32.(71x2-20)
=32. 122
= 3904
c. (11-13)+(15-17)+..+(59-61)
=-2 x 13
=-26