1,So sánh :
A=\(\dfrac{2011+2012}{2012+2013}\) ; B=\(\dfrac{2011}{2012}+\dfrac{2012}{2013}\)
2,Cmr:
\(\dfrac{1}{4.7}+\dfrac{1}{7.10}+...+\dfrac{1}{37.40}< \dfrac{1}{3}\)
So sánh 2 p/số
\(A=\dfrac{2014^{2013}+1}{2014^{2014}+1};B=\dfrac{2014^{2012}+1}{2014^{2013}+1}\)
So sánh
\(A=\dfrac{2011+2012}{2012+2013}\) và \(B=\dfrac{2011}{2012}+\dfrac{2012}{2013}\)
Bài 1. Chứng tỏ rằng: B=\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+\dfrac{1}{5^2}+\dfrac{1}{6^2}+\dfrac{1}{7^2}+\dfrac{1}{8^2}< 1\)
Bài 2. so sánh : A=\(\dfrac{2011+2012}{2012+2013}\)
và B=\(\dfrac{2011}{2012}+\dfrac{2012}{2013}\)
Bài 3. Rút gọn : B= \(\left(1-\dfrac{1}{1}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{20}\right)\)
Bài 4. Rút gọn biểu thức : A= \(1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2012}}\)
Bài 5. Tìm số nguyên \(\pi\) sao cho \(\pi+5\) chia hết cho \(\pi-2\)
HELP ME!!!! MÌNH TICK CHO HA
Tính
P=\(\left(1-\dfrac{28}{10}\right)\left(1-\dfrac{52}{22}\right)\left(1-\dfrac{80}{36}\right)...\left(1-\dfrac{21808}{10900}\right)\)
Q=\(\dfrac{1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2012}}{\dfrac{2013}{1}+\dfrac{2014}{2}+\dfrac{2015}{3}+...+\dfrac{4023}{2011}+\dfrac{4024}{2012}-2012}\)
So sánh :
Tình bày lời giải đầy đủ giúp mk nha
\(A=\dfrac{10^{2014}+1}{10^{2013}+1}\) và b= \(\dfrac{10^{2013}+1}{10^{2012}+1}\)
Tính A : \(\dfrac{5.1+2}{1\left(1+1\right)\left(1+2\right)}\) + \(\dfrac{5.2+2}{2\left(2+1\right)\left(2+2\right)}\) + \(\dfrac{5.3+2}{3\left(3+1\right)\left(3+2\right)}\) + ... + \(\dfrac{5.2013+2}{2013\left(2013+1\right)\left(2013+2\right)}\)
So sánh A và B:
1. A=\(\dfrac{79^{2011} - 5}{79^{2011} + 8}\) và B=\(\dfrac{79^{2012} - 6}{79^{2011} + 7}\)
2. A=\(\dfrac{43}{2011^{2012}}\)+\(\dfrac{79}{2011^{2013}}\) và B=\(\dfrac{79}{2011^{2012}}\)+\(\dfrac{43}{2011^{2013}}\)
3. A=\(\dfrac{2010}{2011}\):\(\dfrac{2011}{2012}\) và B=\(\dfrac{2010+2011}{2011+2012}\)
4. A=\(\dfrac{n}{2n+1}\) và B=\(\dfrac{3n+1}{6n+3}\)
Thanks mấy bạn trước nha!!
So sánh
a) \(\dfrac{21}{52}\) và \(\dfrac{213}{523}\)
b) \(\dfrac{n}{n+1}\)và \(\dfrac{n+2}{n+3}\)
c) \(\dfrac{n}{n+3}\)và \(\dfrac{n-1}{n+4}\)
d) \(A=\dfrac{2^{2012}-1}{2^{2013}-1}\) và \(B=\dfrac{2^{2013}-1}{2^{2014}-1}\)
e) \(D=\dfrac{5^{12}+1}{5^{13}+1}\)và \(E=\dfrac{5^{11}+1}{5^{12}+1}\)