Cho A=1.2.3.....29.30 và B=31.32.33.....59.60. Chứng minh A-B chia hết cho 276
Cho A = 1.2.3......29.30
B = 31.32.33.......59.60
a) Chứng minh: B chia hết cho 230
b) Chứng minh: B - A chia hết cho 61
a.
\(B=(32.34.36...60)(31.33.35....59)\)
\(=(2.16.2.17.2.18...2.30)(31.33.35...59)\)
\(=2^{15}(16.17.18...30)(31.33.35...59)\)
\(=2^{15}(16.18...30)(17.19.21...29)(31.33.35...59)\)
\(=2^{15}(2.8.2.9....2.15)(17.19..29)(31.33...59)\)
\(=2^{15}.2^8(8.9.10...15)(17.19...29)(31.33...59)\)
\(=2^{23}(8.10.12.14)(8.11.13.15).(17.19...29)(31.33...59)\)
\(=2^{23}.(8.10.12.14).T=2^{23}(2^3.2.5.2^2.3.2.7).T\)
\(=2^{23}.(2^7.105)T=2^{30}.105T\vdots 2^{30}\)
b.
\(31\equiv -30\pmod {61}\)
\(32\equiv -29\pmod {61}\)
\(33\equiv -28\pmod {61}\)
...........
\(60\equiv -1\pmod {61}\)
$\Rightarrow 31.32....60\equiv (-30)(-29)(-28)..(-1)\pmod {61}$
Hay $B\equiv A\pmod {61}$
Hay $B-A\equiv 0\pmod {61}$
Tức là $B-A$ chia hết cho $61$
cho A = 1.2.3.........29.30
B = 31.32.33.........59.60
chứng minh rằng B - A chia hết cho 61
Tham khảo thêm tại đây:
https://hoc24.vn/cau-hoi/cho-a-1232930-b-3132335960a-chung-minh-b-chia-het-cho-230b-chung-minh-b-a-chia-het-cho-61.1506388592636
Cho A=1.2.3....29.30
B=31.32.33......59.60
a,Chứng minh rằng:B chia hết cho 230
b,Chứng minh rằng:B-A chia hết cho 61
Cho A = 1.2.3......29.30
B=31.32.33.....60
a,c/m B chia hết cho 230
b,C/m B-A chia hết cho 61
Cho A = 1.2.3......29.30
B = 31.32.33........59.60
a) Chứng minh : B chia hết cho 230
b) Chứng minh : B -A chia hết cho 61.
Cho A=1.2.3.....29.30; B=31.32.33.....59.60
Chứng minh rằng:
a)B chia hết cho \(2^{30}\)
b)B-A chia hết cho 61
Giúp mình nha!!!!!!!!!!
Trong B có
các số 32 ; 34 ; 36 ; 38 ; 40 ; 42 ; 44 ; 46 ; 48 ; 50 ; 52 ; 54 ; 56 ; 58 chia hết cho 2.
32 = 25
34 = 2.17
36 = 2².9
38 = 2.19
40 = 2³.523.5
…………….
Làm cứ thế mà ra tổng cộng 30 số 2
=) B chia hết cho 230
A= 10.11+11.12+12.13+......+29.30
B= 1.2.3+2.3.4+......+49.50.51
\(A=10\cdot11+11\cdot12+12\cdot13+...+29\cdot30\)
\(\Leftrightarrow A=\left(1\cdot2+2\cdot3+3\cdot4+...+29\cdot30\right)-\left(1\cdot2+2\cdot3+3\cdot4+...+9\cdot10\right)\)
\(\Leftrightarrow A=\frac{29\cdot30\cdot31}{3}-\frac{9\cdot10\cdot11}{3}\)
\(\Leftrightarrow A=29\cdot10\cdot31-3\cdot10\cdot11\)
\(\Leftrightarrow A=8990-330\)
\(\Leftrightarrow A=8660\)
\(B=1\cdot2\cdot3+2\cdot3\cdot4+...+49\cdot50\cdot51\)
\(\Leftrightarrow B=\frac{1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot\left(5-1\right)+...+49\cdot50\cdot51\cdot\left(52-48\right)}{4}\)
\(\Leftrightarrow B=\frac{1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot5-1\cdot2\cdot3\cdot4+...+49\cdot50\cdot51\cdot52-48\cdot49\cdot50\cdot51}{4}\)
\(\Leftrightarrow B=\frac{49\cdot50\cdot51\cdot52}{4}\)
\(\Leftrightarrow B=49\cdot50\cdot51\cdot13\)
\(\Leftrightarrow B=1624350\)
Bài 1
1/24.25+1/25.26+...+1/29.30+y:1/3=-4
ai giúp mình ,mình sẽ tick
\(\frac{1}{24.25}+\frac{1}{25.26}+\frac{1}{26.27}+...+\frac{1}{29.30}+y:\frac{1}{3}=-4\)
\(\frac{1}{24}-\frac{1}{25}+\frac{1}{25}-\frac{1}{26}+\frac{1}{26}-\frac{1}{27}+...+\frac{1}{29}-\frac{1}{30}+y:\frac{1}{3}=-4\)
\(\frac{1}{24}-\frac{1}{30}+3y=-4\)
\(\frac{1}{120}+3y=-4\)
\(3y=-4-\frac{1}{120}\)
\(3y=-\frac{481}{120}\)
\(y=-\frac{481}{120}:3\)
\(y=-\frac{481}{360}\)
