Chứng tỏ rằng : a, 13^10-13^11-13^12 : 156 thuộc Z
b, 3+3^2+3^3+....+3^15 : 12 thuộc Z
Cho A = 3/10 + 3/11 + 3/12 + 3/13 + 3/14
Chứng tỏ 1 < A < 2
Chứng tỏ rằng:
A=\(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}\)
Thì 1<A<2
\(Cho\:A=2^1+2^2+2^3+2^4+...+2^{12}+2^{13}.\:\)Chứng tỏ rằng A chia hết cho 3, cho 7 và 15
\(Cho\:C=3+3^2+3^3+3^4+...+3^9\)Chứng tỏ rằng C chia hết cho 13
cho y thuộc Z hãy so sánh
a) 13 x a và 11 x a
b) -15 x (a - 3) và -12 x (a - 3)
Xét 3 TH:
+) a âm => 13a-11a=2a<0 ( vì a âm) => 13a<11a
+) a=0 => 11a=13a
+) a dương => 11a-13a=-2a<0 (vì a dương) => 13a>11a
b) tương tự nhé~~~
mọi người ơi pls help me
1) -10/11 . 8/9 + 7/18 . 10/11 2) 12/25 . 23/7 - 12/7 . 13/25 3) 3/7 . 16/15 - 2/15 . -3/7 4) -4/13 . 5/17 + -12/13 . 4/17
\(1)\)\(-\dfrac{10}{11}.\dfrac{8}{9}+\dfrac{7}{18}.\dfrac{10}{11}\)
\(=\dfrac{10}{11}\left(-\dfrac{8}{9}+\dfrac{7}{18}\right)\)
\(=\dfrac{10}{11}\left(\dfrac{-16}{18}+\dfrac{7}{18}\right)\)
\(=\dfrac{10}{11}.\left(-\dfrac{1}{2}\right)=-\dfrac{5}{11}\)
\(2)\)\(\dfrac{12}{25}.\dfrac{23}{7}-\dfrac{12}{7}.\dfrac{13}{25}\)
\(=\dfrac{12}{7}.\dfrac{23}{25}-\dfrac{12}{7}.\dfrac{13}{25}\)
\(=\dfrac{12}{7}.\left(\dfrac{23}{25}-\dfrac{13}{25}\right)\)
\(=\dfrac{12}{7}.\dfrac{2}{5}=\dfrac{24}{35}\)
\(3)\)\(\dfrac{3}{7}.\dfrac{16}{15}-\dfrac{2}{15}.\dfrac{-3}{7}\)
\(=\dfrac{3}{7}.\dfrac{16}{15}-\dfrac{3}{7}.\dfrac{-2}{15}\)
\(=\dfrac{3}{7}.\left(\dfrac{16}{15}+\dfrac{2}{15}\right)\)
\(=\dfrac{3}{7}.\dfrac{18}{15}=\dfrac{18}{35}\)
\(4)\)\(-\dfrac{4}{13}.\dfrac{5}{17}+\dfrac{-12}{13}.\dfrac{4}{17}\)
\(=-\dfrac{4}{13}.\dfrac{5}{17}+\dfrac{-4}{13}.\dfrac{12}{17}\)
\(=-\dfrac{4}{13}.\left(\dfrac{5}{17}+\dfrac{12}{17}\right)\)
\(=-\dfrac{4}{13}.\dfrac{17}{17}=-\dfrac{4}{13}\)
`#040911`
`1)`
`-10/11 * 8/9 + 7/18 . 10/11`
`= 10/11 * (-8/9 + 7/18)`
`= 10/11 * (-1/2)`
`= -5/11`
`2)`
`12/25 * 23/7 - 12/7 *13/25`
`= 12/7 * 23/25 - 12/7 * 13/25`
`= 12/7 * (23/25 - 13/25)`
`= 12/7 * 2/5`
`= 24/35`
`3)`
`3/7 * 16/15 - 2/15 * (-3)/7`
`= 3/7 * (16/15 + 2/15)`
`= 3/7 * 6/5`
`= 18/35`
`4)`
`-4/13 * 5/17 + (-12)/13 * 4/17`
`= -4/17 * 5/13 + (-12)/13 * 4/17`
`= 4/17 * (-5/13 - 12/13)`
`= 4/17 * (-17)/13`
`= -4/13`
Cho A= 3/10 + 3/11 + 3/12 + 3/13 + 3/14. Chứng minh rằng: 1 < A < 2
1.tìm x
a)(x=1/4-1/3):(2+1/6-1/4)=7/40
b)13/15-(13/21+x).7/12=7/10
c)(-5/3)^3<x<-24/35.-5/6(x thuộc Z)
Tìm x thuộc Z;
a) 12+11+10+....+(x+1)+x =-13
b) x+(x+1)+(x+2)+....+2008+2009=2009
c) 196 +1962+....+(x+1)+x=3925
d) -12 (x-5)+7 (3-x)=5
e) 2 (x-3) - 3 (2-3x)=4 [(1-2x)+15]
f) 3 (x-1) - (x-5) = -15
g) 5 (x-2) - ( x+3)+15
h) /x+1/=a (a thuộc Z)
Giúp mình nhé mình đang gấp lắm. Cảm ơn rất nhiều
a) \(4^{13}+4^{14}+4^{15}+4^{16}=4^{13}\left(1+4\right)+4^{14}\left(1+4\right)=4^{13}.5+4^{14}.5=5\left(4^{13}+4^{14}\right)⋮5\Rightarrow dpcm\)
c) \(2^{10}+2^{11}+2^{12}+2^{13}+2^{14}+2^{15}\)
\(=2^{10}\left(1+2+2^2\right)+2^{13}\left(1+2+2^2\right)\)
\(=2^{10}.7+2^{13}.7=7\left(2^{10}+2^{13}\right)⋮7\Rightarrow dpcm\)
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