Cho B = 3/10 + 3/11 + 3/12 + 3/13 + 3/14. Chứng tỏ 1 < B < 2
Chứng tỏ A chia hết cho 13
A=1+2+2^2+2^3+...+2^11
Theo đề bài ta có:
A = \(1+2+2^2+2^3+...+2^{11}\)
\(\Rightarrow A=2^0+2^1+2^2+2^3+...+2^{11}\)
\(\Leftrightarrow A=2^0.\left(1+2+2^2+2^3+2^4+2^5\right)+2^6.\left(1+2+2^2+2^3+2^4+2^5\right)\)
\(\Rightarrow A=2^0.63+2^6.63\)
\(\Rightarrow A=63.\left(2^0+2^6\right)\)
\(\Rightarrow A=63.65\)
Vậy A chia hết cho 13 ( vì 65 chia hết cho 13)
Chứng tỏ rằng 27^10 + 3^29 - 9^14 chia hết cho 13
Cho tổng S = 3+3^2+3^3+3^4+...+3^2015
a) Tính S b) Chứng tỏ Schia hết cho 13
Ta có :
S=3+32+33+34+....+32015
3S=32+33+34+35+....+32016
3S-S=(32+33+34+35+....+32016)-(3+32+33+....+32015)
2S=32016-3
S=(32016-3):2
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) \(2^{10}+2^{11}+2^{12}+2^{13}+2^{14}+2^{15}\)
\(=2^{10}\left(1+2+2^2\right)+2^{13}\left(1+2+2^2\right)\)
\(=2^{10}.7+2^{13}.7=7\left(2^{10}+2^{13}\right)⋮7\Rightarrow dpcm\)
Câu c bạn xem lại đê
Cho M = 1+3+32+33+...+313. Chứng tỏ M chia hết cho 13
Ta có: M=1+3+3^2+...+3^13
=(1+3+3^2)+(3^3+3^4+3^5)+...+(3^11+3^12+3^13)
=13+3^3.(1+3+3^2)+..+3^11.(1+3+3^2)
=13+3^3.13+...+3^11.13
=13.(1+3^3+..+3^11) ( chia het cho 13)
Vay M chia het cho 13
chứng tỏ rắng C=1+ 3+3^2+.......+3^11 chia hết cho 40
\(C=1+3+3^2+....+3^{11}\)
\(C=\left(1+3+3^2+3^3\right)+\left(3^4+3^5+3^6+3^7\right)+\left(3^8+3^9+3^{10}+3^{11}\right)\)
\(C=40.1+40.3^4+40.3^8\)
\(C=40.\left(1+3^4+3^8\right)\)
CHia hết cho 40
C=1+3+32+33+...+311
=(1+3+32+33)+...+(38+39+310+311)
=40+....+38(1+3+32+33)
=40+...+38.40=40(1+...+38) chia hết cho 40
=>đpcm
C=(1+3+3^2+3^3)+(3^4+3^5+3^6+3^7)+(3^8+3^9+3^10+3^11)
=40+40.3^4+40.3^8
=40.(1+3^4+3^8) chia hết cho 40
a)Cho A= 3/10+3/11+3/12+3/13+3/14.
Chứng minh A<3/2
b)Cho B=1/11+1/12+1/13+....+1/20.
Chứng minh 7/12<B<5/6c
c)Cho C=1/5+1/6+....+1/17
Chứng minh C>1
cho S=3/10+3/11+3/12+3/13+3/14 CMR 1<S<2
3/10>3/15
3/11>3/15
3/12>3/15
3/13>3/15
3/14>3/15
=>S>3/15*5=15/15=1
3/11<3/10
3/12<3/10
3/13<3/10
3/14<3/10
=>3/11+3/12+3/13+3/14+3/10<3/10*5=15/10=3/2<2
=>1<S<2
AI BIẾT LÀM BÀI NÀY CHỈ GIÚP EM VỚI Ạ!!!
Cho A = 3 + 3^2 + 3^3 +..... + 3^60. Chứng tỏ rằng:
a) A chia hết cho 4
b) A chia hết cho 13
a) \(A=3+3^2+..+3^{60}\)
\(A=\left(3+3^2\right)+\left(3^3+3^4\right)+...+\left(3^{59}+3^{60}\right)\)
\(A=3\cdot\left(1+3\right)+3^3\cdot\left(1+3\right)+...+3^{59}\cdot\left(1+3\right)\)
\(A=4\cdot\left(3+3^3+...+3^{59}\right)\)
Vậy A chia hết cho 4
b) \(A=3+3^2+3^3+...+3^{60}\)
\(A=\left(3+3^2+3^3\right)+...+\left(3^{58}+3^{59}+3^{60}\right)\)
\(A=3\cdot\left(1+3+3^2\right)+...+3^{58}\cdot\left(1+3+3^2\right)\)
\(A=13\cdot\left(3+..+3^{58}\right)\)
Vậy A chia hết cho 13