H = 1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + ... + 2^2009
k = 2^2010 - 1
So sanh k va H
1so sanh phan so
33/28 va 24/27 23/28 va 24/27 415 /395 va 572/571
2 tinh
4 -3/2 x1/8 + 2/5 7/4 - 1/3 : 2/7 + 1/6 3/2 x 1/3 + 4/7 + 1/2 3/4 : 2 + 1/3 + 1/6
so sanh 2^1+2^2+2^3+...+2^2010 va 2^2010+1
Bài 1:
a) C/m: A=2^1+2^2+2^3+2^4+....+2^2010 chia het cho 3 và 7
b) C/m: B=3^1+3^2+3^3+3^4+....+3^2010 chia het cho 4 va 13
c) C/m: C= 5^1+5^2+5^3+5^4+....+5^2010 chia het cho 6 va 31
d) C/m: D=7^1+7^2+7^3+7^4+....+7^2010 chia het cho 8 va 57
1so sanh cac phan so sau
a,2/3 va -1/4
b -7/10 va 7/-8
c 6/7 va 3/5
d -14/21 va 60/-72
e 16/9 va24/13
g 27/82 va 26/75
Tinh hợp lý các biểu thức sau:
F=1-2+3-4+....+2009+2010
G=0-2+4-6+...+2010-2010
H=13-12+11+10-9+8-7-6+5-4-3+2-1
I=1-2-3+4+5-6-7-8+9...+2001-2002-2003+2004+2005+2006
J=1+2-3-4+6+6-7-8+9+...+2002-2003-2004+2005+2006
So sanh : .A=2^0+2^1+2^2+2^3+...+2^2010 va` B=2^2011-1.
Có A=20+21+22+23+24+.....+22010
Nên 2A = 2 (20+21+22+23+24+.....+22010 )
= 21+22+23+24+.....+22011 + 22011
=>A = 2A - A = 22011 - 20
= 22011 - 1
= B
Vậy A = B
so sanh a va b co bang nhau ko
a = 1^2 + 5^2 +6^2 b = 2^2 +3^2 +7^2
a= 10^2 +11^2 +12^2 b= 13^2 +14^2
a= 17 x (3+ 7 ) va b= 3^3 +7^3
a=4 x (4+8 ) va b= 4^3 +8^3
cho A= 3+2^2+2^3+...+2^2010+2^2011,B=2^2012.so sanh A va B
cho A= 3+2^2+2^3+...+2^2010+2^2011,B=2^2012.so sanh A va B
2A = 6+2^3+2^4+.....+2^2012
A = 2A - A = (6+2^3+2^4+.....+2^2012)-(3+2^2+2^3+......+2^2011)
= 6+2^2012 - 3 - 2^2
= 2^2012 - 1
=> A < B
Tk mk nha
ta có :
\(A=3+2^2+2^3+.....+2^{2011}.\)
\(\Rightarrow2A=6+2^3+2^4+....+2^{2012}\)
\(\Rightarrow A=\left(6+2^3+2^4+...+2^{2012}\right)-\left(3+2^2+2^3+....+2^{2011}\right)\)
\(\Rightarrow A=-1+2^{2012}\)
vì -1+2^2012<2^2012 nên A <B