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B = 31 + 32 + 33 + ... + 328 + 329 + 330
B = ( 31 + 32 + 33 ) + ... + ( 328 + 329 + 330 )
B = 31 . ( 1 + 3 + 32 ) + ... + 328 . ( 1 + 3 + 32 )
B = 31 . 13 + ... + 328 . 13
B = 13 . ( 3 + ... + 328 ) \(⋮\)13
Vậy B \(⋮\)13 ( dpcm )
\(B=3^1+3^2+3^3+3^4+3^5+............+3^{30}\)
\(\Rightarrow B=\left(3^1+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+............+\left(3^{28}+3^{29}+3^{30}\right)\)
\(\Rightarrow B=3^1.\left(1+3+3^2\right)+3^4.\left(1+3+3^2\right)+.........+3^{28}.\left(1+3+3^2\right)\)
\(\Rightarrow B=3^1.13+3^4.13+.........+3^{28}.13\)
\(\Rightarrow B=13\left(3^1+3^4+.........+3^{28}\right)\)
Mà 13 \(⋮\)13 \(\Rightarrow13\left(3^1+3^4+...........+3^{28}\right)⋮13\)
Vậy B chia hết cho 13
a: \(=\dfrac{20\left(1-12\right)}{30\left(-1-10\right)}=\dfrac{2}{3}\)
b: \(=\dfrac{11^9\cdot3^{18}}{3^{18}\cdot11^{11}}=\dfrac{1}{121}\)
a: \(=\dfrac{20\left(1-12\right)}{30\left(-1-10\right)}=\dfrac{20}{30}=\dfrac{2}{3}\)
b: \(=\dfrac{11^9\cdot3^{18}}{3^{10}\cdot11^{11}\cdot3^8}=\dfrac{1}{121}\)
1)
a) -(2+5) = -2 - 5 = -7
b) +(-3+6) = -3 + 6 = 3
c) (-50+3) = -50 + 3 = -47
d) -(-2+3) = 2 - 3 = -1
e) -(10-3) = -10 + 3 = -7
f) -(-3)-(-3+1) = 3 + 3 - 1 = 5
g) (-5)+(-2+10) = -5 - 2 + 10 = 3
2)
a) -50+120+(-150)-20+30
= -(50 + 20) + (120 + 30 - 150)
= -70
b) 265-70+(-65)-30+15
= (265 - 65) - (70 + 30) + 15
= 200 - 100 + 15 = 115
c) -17+185-183+(-85)-63
= (185 - 85) - (183 + 17) - 63
= 100 - 200 - 63 = -163
d) -30+60+(-170)-260+19
= -(170 + 30) - (260 - 60) + 19
= -200 - 200 + 19 = -381
(59-5^30)-(59+3^3-5^30)
=[(59-5^30)-(59-5^30)]+3^3
=0+9
=9
390:13=30