SO SÁNH
A, A=\(\frac{2015^{2015}+1}{2015^{2014}+1}VÀB=\frac{2015^{2014}+1}{2015^{2013}+1}\)
B, B= \(\frac{2010^{2015}+1}{2010^{2016}+1}VÀC=\frac{2010^{2014}+1}{2010^{2015}+1}\)
\(SOSANH\)
\(A=\frac{2010^{2015}+1}{2010^{2016}+1}VÀB=\frac{2010^{2014}+1}{2010^{2015}+1}\)
SO SÁNH
ạ, A = \(A=\frac{2015^{2015}+1}{2015^{2014}+1}VÀB=\frac{2015^{2014}+1}{2015^{2013}+1}\)
Cho A = \(\frac{2000}{2001}+\frac{2001}{2002}+\frac{2002}{2003}+\frac{2003}{2004}+\frac{2005}{2006}+\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}+\frac{2015}{2016}\)
Hãy so sánh tổng các phân số trong A và so sánh với 15.
mỗi số hạng trong biểu thức A đều nhỏ hơn 1 mà có 15 số nên tổng A sẽ nhỏ hơn 15
ta thay tong tren <1+1+1+1+1+1+1+1+1+1+1+1+1+1+1
hay tong tren be hon 15
Không tính cụ thể , hãy sắp xếp các biểu thức sau theo thứ tự giảm dần :
\(\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}\)
\(\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}\)
\(\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}\)
\(\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}\)
\(\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}\)
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$
So sánh : \(A=\frac{2015^{2016}+1}{2015^{2015}+1}\) và \(B=\frac{2014^{2015}+1}{2014^{2014}+1}\)
A = \(\frac{2015^{2016}+1}{2015^{2015}+1}=\frac{2015^{2015}+1}{2015^{2015}+1}+\frac{2015}{2015^{2015}+1}=1+\frac{2015}{2015^{2015}+1}\)
B = \(\frac{2014^{2015}+1}{2014^{2014}+1}=\frac{2014^{2014}+1}{2014^{2014}+1}+\frac{2014}{2014^{2014}+1}=1+\frac{2014}{2014^{2014}+1}\)
Rồi bạn tự so sánh nha
1) CMR : A=(n+2015)(n+2016) + n2 + n chia hết cho 2 với n ϵ N
2) So sánh :
P = \(\frac{2013}{2014^{2013}}+\frac{2014}{2015^{2014}}+\frac{2015}{2016^{2015}}+\frac{2016}{2017^{2016}}\) và
Q = \(\frac{2014}{2017^{2016}}+\frac{2013}{2016^{2015}}+\frac{2016}{2015^{2014}}+\frac{2015}{2014^{2013}}\)
A = (n + 2015)(n + 2016) + n2 + n
= (n + 2015)(n + 2015 + 1) + n(n + 1)
Tích 2 số tự nhiên liên tiếp luôn chia hết cho 2
=> (n + 2015)(n + 2015 + 1) chia hết cho 2
n(n + 1) chia hết cho 2
=> (n + 2015)(n + 2015 + 1) + n(n + 1) chia hết cho 2
=> A chia hết cho 2 với mọi n \(\in\) N (đpcm)
So sánh:\(A=\frac{10^{2015}-1}{10^{2016}-1}vàB=\frac{10^{2014}+1}{10^{2015}+1}\)
So sánh A=\(\frac{2014^{2015}+1}{2014^{2015}+1}\) va B=\(\frac{2014^{2014}+1}{2014^{2013}+1}\)
Ta có :
\(\frac{2014^{2015}+1}{2014^{2015}+1}\)\(=1\)
\(\frac{2014^{2014}+1}{2014^{2013}+1}\)\(>1\)
\(\Rightarrow A< B\)
Vậy \(A< B\)
So sánh:
A=\(\frac{2015^{2013}+1}{2015^{2014}+1}\)
B=\(\frac{2015^{2015}+1}{2015^{2016}+1}\)
\(A=\frac{2015^{2013}+1}{2015^{2014}+1}=\frac{\left(2015^{2013}+1\right)\left(2015^{2014}+1\right)}{\left(2015^{2014}+1\right)\left(2015^{2016}+1\right)}=\frac{2015^{4027}+2015^{2013}+2015^{2014}+1}{\left(2015^{2014}+1\right)\left(2015^{2016}+1\right)}\)
\(B=\frac{2015^{2015}+1}{2015^{2016}+1}=\frac{\left(2015^{2015}+1\right)\left(2015^{2014}+1\right)}{\left(2015^{2016}+1\right)\left(2015^{2014}+1\right)}=\frac{2015^{4029}+2015^{2015}+2015^{2014}+1}{\left(2015^{2016}+1\right)\left(2015^{2014}+1\right)}\)
Ta thấy hiển nhiên thử của B > tử của A nên B > A
Vậy...