2012\(\times\)1001- 2012+2013\(\times\)999+2013
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= 2012 x (1001-1) + 2013 x (999+1)
= 2012 x 1000 + 2013 x 1000
= 1000 x (2012+2013)
= 1000 x 4025 = 4025000
k mk nha
= 2012 x (1001-1) + 2013 x (999+1)
= 2012 x 1000 + 2013 x 1000
= 1000 x (2012+2013)
= 1000 x 4025 = 4025000
g: \(B=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{19}{20}=\dfrac{1}{20}\)
h: \(=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot..\cdot\dfrac{100}{99}=\dfrac{100}{2}=50\)
f: \(A=1+\dfrac{1}{2^{2014}}\)
\(B=\dfrac{2^{2014}+1+1}{2^{2014}+1}=1+\dfrac{1}{2^{2014}+1}\)
mà \(2^{2014}< 2^{2014}+1\)
nên A>B
2013×20122012-2012×20132013
= (2013 . 20122012) - ( 2012 . 20132013)
= 40505610156 - 40505610156
= 0
2013×20122012-2012×20132013
= (2013 . 20122012) - ( 2012 . 20132013)
= 40505610156 - 40505610156
= 0
\(\left(1-\frac{1}{7}\right).\left(1-\frac{1}{8}\right).\left(1-\frac{1}{9}\right)......\left(1-\frac{1}{2011}\right)\)
\(=\frac{6}{7}.\frac{7}{8}.\frac{8}{9}.....\frac{2010}{2011}\)
\(=\frac{6.7.8.9.....2010}{7.8.9.10.....2011}\)
\(=\frac{6}{2011}\)
\(2012M=\frac{2012^{2013}}{2013^{2013}}=\frac{2012}{2013}\)
=>\(M=\frac{2012}{2013}:2012=\frac{1}{2013}\)
\(2012N=\frac{2012\left(2012^{2012}+2012\right)}{2013^{2013}+2013}=\frac{2012^{2013}+2012^2}{2013^{2013}+2013}\)
=>\(N=\frac{2012+2012^2}{2013+2013}:2012=\frac{4050156}{4026}:2012=\frac{1}{2}\)
=>\(\frac{1}{2013}< \frac{1}{2}\) (vì phân số nào có mẫu bé hơn thì phân số đó lớn hơn)
=> M < N
Ta có : 2012 x 1001 - 2012 + 2013 x 999 + 2013
= 2012 x (1001 - 1) + 2013 x (999 + 1)
= 2012 x 1000 + 2013 x 1000
= 1000 x (2012 + 2013)
= 1000 x 4025
= 4 025 000
=2014012-2012+2010987+2013
=2012000+2010987+2013
=4025000