So Sánh
a,A= \(\frac{2008^{2008}+1}{2008^{2009}+1}\)và B=\(\frac{2008^{2007}+1}{2008^{2008}+1}\)
b, M=\(\frac{100^{100}+1}{100^{99}+1}\)và N= \(\frac{100^{101}+1}{100^{100}+1}\)
Những câu hỏi liên quan
1. So sánh A và B
A= 20082007 +1/ 20082008 + 1
B= 20082007 + 1/ 20082008 +1
2. So sánh M và N
M= 100100 + 1/ 10099 +1
N= 100101 +1/ 100100+1
3. Cm:
B= 5^2008 +5^2007 +5^2006 chia hết cho 31.
C= 8^8 +2^20 chia hết cho 17.
D= 313^5 . 299- 313^6 . 36 chia hết cho 7
So sánh A và B biết:\(A=\frac{100^{2007}+1}{100^{2008}+1};B=\frac{100^{2006}+1}{100^{2007}+1}\)
Xin chào các bạn !!!
Hãy Đăng Kí Cho Channel Kaito1412_TV Để nhé !
Link là : https://www.youtube.com/channel/UCqgS-egZEJIX-ON873XpD_Q/videos?view_as=subscriber
Đúng 0
Bình luận (0)
So sánh:
a, A= 1315+1/1316+1 và B= 20082007+1/20082008+1
b, A= 100100+1/10099+1 và B= 100101+1/100100+1
1. \(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{99}}+\frac{1}{2^{100}}+\frac{1}{2^{100}}\)
2. So sánh: \(\dfrac{2008}{2009}+\dfrac{2009}{2010}\) và \(\dfrac{2008+2009}{2009+2010}\)
1.
\(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{99}}+\frac{1}{2^{100}}+\frac{1}{2^{100}}\)
\(=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{99}}+\left(\frac{1}{2^{100}}+\frac{1}{2^{100}}\right)\)
\(=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{99}}+\frac{1}{2^{99}}\)
cứ làm như vậy ta được :
\(=1+1=2\)
Đúng 0
Bình luận (0)
2. Ta có :
\(\frac{2008+2009}{2009+2010}=\frac{2008}{2009+2010}+\frac{2009}{2009+2010}\)
vì \(\frac{2008}{2009}>\frac{2008}{2009+2010}\); \(\frac{2009}{2010}>\frac{2009}{2009+2010}\)
\(\Rightarrow\frac{2008}{2009}+\frac{2009}{2010}>\frac{2008+2009}{2009+2010}\)
Đúng 0
Bình luận (0)
Cho A =\(\frac{100^{2007}+1}{100^{2008}+1}\)và cho B=\(\frac{100^{2006}+1}{100^{2007}+1}\).Hãy so sánh A và B
\(A=\frac{100^{2007}+1}{100^{2008}+1}\Rightarrow100.A=\frac{100^{2008}+100}{100^{2008}+1}=\frac{100^{2008}+1+99}{100^{2008}+1}=1+\frac{99}{100^{2008}+1}\)
\(B=\frac{100^{2006}+1}{100^{2007}+1}\Rightarrow100.B=\frac{100^{2007}+100}{100^{2007}+1}=\frac{100^{2007}+1+99}{100^{2007}+1}=1+\frac{99}{100^{2007}+1}\)
Vì \(\frac{99}{100^{2007}+1}>\frac{99}{100^{2008}+1};1=1\Rightarrow1+\frac{99}{100^{2007}+1}>1+\frac{99}{100^{2008}+1}\)hay \(A>B\)
Vậy \(A>B\)
Đúng 0
Bình luận (0)
Bài 1: So sánh A và B
\(A=\frac{2008^{2008}+1}{2008^{2009}+1}\)
\(B=\frac{2008^{2007}+1}{2008^{2008}+1}\)
1.A=(2/3+3/4+4/5+................+99/100)*(1/2+2/3+..............+98/99);B=(1/2+2/3+..............+99/100)*(2/3+3//4+...................+98/99)
Tính A và B bằng cách thuận tiện nhất.
2.Cho a=2008/2009;b=2009/2008;c=1/2009;d=2007/2008
Tính a-b+c+d
3.Tìm STN m biết:
2016+m/m+2520+m/m+3024+m/m
So sánh A vs B
\(A=\frac{2008^{2008}+1}{2008^{2009}+1}\)
\(B=\frac{2008^{2007}+1}{2008^{2008}+1}\)
ý, nếu không được dùng cách kia thì làm cách này cho chắc đi :v
Ta có: \(2008A=\frac{2008\left(2008^{2008}+1\right)}{2008^{2009}+1}=\frac{2008^{2009}+2008}{2008^{2009}+1}=\frac{\left(2008^{2009}+1\right)+2007}{2008^{2009}+1}=1+\frac{2007}{2008^{2009}+1}\)
Lại có: \(2008B=\frac{2008\left(2008^{2007}+1\right)}{2008^{2008}+1}=\frac{2008^{2008}+2008}{2008^{2008}+1}=\frac{\left(2008^{2008}+1\right)+2007}{2008^{2008}+1}=1+\frac{2007}{2008^{2008}+1}\)
Vì 2008 < 2009 \(\Rightarrow2008^{2008}< 2008^{2009}\)\(\Rightarrow2008^{2008}+1< 2008^{2009}+1\)\(\Rightarrow\frac{2007}{2008^{2008}+1}>\frac{2007}{2008^{2009}+1}\)\(\Rightarrow1+\frac{2007}{2008^{2008}+1}>1+\frac{2007}{2008^{2009}+1}\)\(\Rightarrow2008B>2008A\)\(\Rightarrow B>A\)
Vì A <1 , B < 1
Nên ta có: \(A=\frac{2008^{2008}+1}{2008^{2009}+1}< \frac{2008^{2008}+1+2007}{2008^{2009}+1+2007}=\frac{2008^{2008}+2008}{2008^{2009}+2008}=\frac{2008\left(2008^{2007}+1\right)}{2008\left(2008^{2008}+1\right)}=\frac{2008^{2007}+1}{2008^{2008}+1}=B\)
So sánh cặp số sau:
\(A=\frac{2006^{2007}+1}{2007^{2008}+1};B=\frac{2007^{2008}+1}{2008^{2009}+1}\)
Giúp!!!
A=\(\frac{2007^{2007}}{2008^{2008}}\)
B=\(\frac{2008^{2008}}{2009^{2009}}\)
Đúng 0
Bình luận (0)
