So sánh:
A=\(\frac{10^{2012}-10}{10^{2013}-10}\)
B=\(\frac{10^{2011}+10}{10^{2012}+10}\)
bai 1:tính nhanh : P=\(\frac{\frac{2}{3}-\frac{1}{4}+\frac{5}{11}}{\frac{5}{12}+1-\frac{7}{11}}\)
Bai 2:Thực hiện phép tính: 1-2+3-4+5-6+...+2011-2012
Bai 3:so sánh:A=\(\frac{2011+2012}{2012+2013}\)
B=\(\frac{2011}{2012}+\frac{2012}{2013}\)
bai4:so sánh:A=\(\frac{20^{10}+1}{20^{10}-1}\)
B=\(\frac{20^{10}-1}{20^{10}-3}\)
Bài 2:1-2+3-4+...+2011-2012
=1+2+3+4+...+2011+2012-2(2+4+6+...+2012)
=2025078-2(1012036)
=2025078-2024072
=1006
Học giỏi!
So sánh:
a) \(\frac{2^{10}+1}{2^{10}-1}\)và \(\frac{2^{10}-1}{2^{10}-3}\)
b) \(\frac{2011}{2012}+\frac{2012}{2013}\)và \(\frac{2011+2012}{2012+2013}\)
a) \(\frac{2^{10}+1}{2^{10}-1}\)và \(\frac{2^{10}-1}{2^{10}-3}\)
Ta có chính chất phân số trung gian là \(\frac{2^{10}+1}{2^{10}-3}\)
\(\frac{2^{10}+1}{2^{10}-1}>\frac{2^{10}+1}{2^{10}-3}\) ; \(\frac{2^{10}-1}{2^{10}-3}< \frac{2^{10}+1}{2^{10}-3}\)
Vì \(\frac{2^{10}+1}{2^{10}-1}>\frac{2^{10}+1}{2^{10}-3}>\frac{2^{10}-1}{2^{10}-3}\)
Nên \(\frac{2^{10}+1}{2^{10}-1}>\frac{2^{10}-1}{2^{10}-3}\)
b) \(A=\frac{2011}{2012}+\frac{2012}{2013}\)và \(B=\frac{2011+2012}{2012+2013}\)
Ta có : \(A=\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2013}+\frac{2012}{2013}=\frac{2011+2012}{2013}>\frac{2011+2012}{2012+2013}=B\)
Vậy A > B
Có gì sai cho sorry
a,
\(\frac{2^{10}+1}{2^{10}-1}=1+\frac{2}{2^{10}-1}< 1+\frac{2}{2^{10}-3}=\frac{2^{10}-1}{2^{10}-3}\)
b,
\(\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2012+2013}+\frac{2012}{2012+2013}=\frac{2011+2012}{2012+2013}\)
So sánh A và B
\(A=\frac{10^{2011}+1}{10^{2012}+1};B=\frac{10^{2012}+1}{10^{2013}+1}\)
So sánh A=\(\frac{10^{2011}+1}{10^{2012}+1}\)và B=\(\frac{10^{2012}+1}{10^{2013}+1}\)
\(B< \frac{10^{2012}+1+9}{10^{2013}+1+9}=\frac{10^{2012}+10}{10^{2013}+10}=\frac{10\left(10^{2011}+1\right)}{10\left(10^{2012}+1\right)}=\frac{10^{2011}+1}{10^{2012}+1}=A\)
Vậy A > B
Áp dụng bất đẳng thức :
\(\frac{a}{b}< 1\Leftrightarrow\frac{a}{b}< \frac{a+m}{b+m}\)
Ta có :
\(B=\frac{10^{2012}+1}{10^{2013}+1}< \frac{10^{2012}+1+9}{10^{2013}+1+9}=\frac{10^{2012}+10}{10^{2013}+10}=\frac{10\left(10^{2011}+1\right)}{10\left(10^{2012}+1\right)}=\frac{10^{2011}+1}{10^{2012}+1}=A\)
\(\Leftrightarrow B< A\)
So sánh 2 phân số sau \(\frac{10^{2011}+10}{10^{2012}+10}v\text{à}\frac{10^{2012}-10}{10^{2013}-10}\)
đặt A=\(\frac{10^{2011}+10}{10^{2012}+10}\)
=>10A=\(\frac{10\left(10^{2011}+10\right)}{10^{2012}+10}=\frac{10^{2012}+100}{10^{2012}+10}=\frac{10^{2012}+10}{10^{2012}+10}+\frac{90}{10^{2012}+10}=1+\frac{90}{10^{2012}+10}\)
đặt B=\(\frac{10^{2012}-10}{10^{2013}-10}\)
=>10B=\(\frac{10\left(10^{2012}-10\right)}{10^{2013}-10}=\frac{10^{2013}-100}{10^{2013}-10}=\frac{10^{2013}-10}{10^{2013}-10}+\frac{-90}{10^{2013}-10}=1+\frac{-90}{10^{2013}-10}\)
vì \(\frac{-90}{10^{2013}-10}\) luôn âm nên
\(1+\frac{90}{10^{2012}+10}>1+\frac{-90}{10^{2013}-10}\)
vậy \(A>Bhay\frac{10^{2011}+10}{10^{2012}+10}>\frac{10^{2012}-10}{10^{2013}-10}\)
dễ mà cũng hỏi à mình học lớp 4 đó
Bài 7 : a, Không quy đồng hãy tính tổng sau :
\(A=\frac{-10}{20}+\frac{-10}{30}+\frac{-10}{42}+\frac{-10}{56}+\frac{-10}{72}+\frac{-10}{90}+\frac{-10}{110}\)
b, So sánh P và Q biết :
\(P=\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\) và \(Q=\frac{2010+2011+2012}{2011+2012+2013}\)
b,Ta có
\(\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\)
\(\frac{2011}{2012}>\frac{2011}{2011+2012+2013}\)
\(\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\)
\(\Rightarrow P>Q\)
\(A=\frac{-10}{20}+\frac{-10}{30}+\frac{-10}{42}+\frac{-10}{56}+\frac{-10}{72}+\frac{-10}{90}+\frac{-10}{110}\)
\(=-10\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}\right)\)
\(=-10\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}\right)\)
\(=-10\left(\frac{1}{4}-\frac{1}{11}\right)\)
\(=\frac{-35}{22}\)
So sánh A và B biết:
\(A=\frac{10^{2011}+1}{10^{2012}+1};B=\frac{10^{2012}+1}{10^{2013}+1}\)
So sánh 2 phân số sau $\frac{10^{2011}+10}{10^{2012}+10}v\text{à}\frac{10^{2012}-10}{10^{2013}-10}$102011+10102012+10 và102012−10102013−10
kick dzô chữ xanh là được!! OK
Ta có :
10. A = \(\frac{10.\left(10^{2011}+1\right)}{10^{2012}+1}\)
= \(\frac{10^{2012}+10}{10^{2012}+1}\)
= \(\frac{10^{2012}+1+9}{10^{2012}+1}\)
= \(\frac{10^{2012}+1}{10^{2012}+1}-\frac{9}{10^{2012}+1}\)
= 1 - \(\frac{9}{10^{2012}+1}\)
10 . B = \(\frac{10.\left(10^{2012}+1\right)}{10^{2013}+1}\)
= \(\frac{10^{2013}+10}{10^{2013}+1}\)
= \(\frac{10^{2013}+1+9}{10^{2013}+1}\)
= 1 - \(\frac{9}{10^{2013}+1}\)
Vì \(\frac{9}{10^{2012}+1}\) >\(\frac{9}{10^{2013}+1}\) nên 10.A > 10.B
=> A >B
Vậy ...........
So sánh A và B biết:
A= \(\frac{10^{2011}+1}{10^{2012}+1}\); B= \(\frac{10^{2012}+1}{10^{2013}+1}\)
Áp dụng a/b < 1 => a/b < a+m/b+m (a,b,m thuộc N*)
\(=>B=\frac{10^{2012}+1}{10^{2013}+1}< \frac{10^{2012}+1+9}{10^{2013}+1+9}\)
\(< \frac{10^{2012}+10}{10^{2013}+10}\)
\(< \frac{10.\left(10^{2011}+1\right)}{10.\left(10^{2012}+1\right)}\)
\(< \frac{10^{2011}+1}{10^{2012}+1}=A\)
=> B < A
Ủng hộ mk nha ^_-
1.so sánh
a)cho A=\(\frac{10^{2001}+1}{10^{2002}+1}\) ; B=\(\frac{10^{2002}+1}{10^{2003}+1}\) hãy so sánh A và B
b)C=\(\frac{196}{197}+\frac{197}{198}\) và D=\(\frac{196+197}{197+198}\)
c)E=\(\frac{2011+2012}{2012+2013}\) và F=\(\frac{2011}{2012}+\frac{2012}{2013}\)
a)
\(10A=\frac{10^{2002}+10}{10^{2002}+1}=1+\frac{9}{10^{2002}+1}\)
\(10B=\frac{10^{2003}+10}{10^{2003}+1}=1+\frac{9}{10^{2003}+1}\)
=> 10A > 10B => A > B