Tìm x biết : 2016^(2x-3).2016^4 = 2010.2016^4
Các bn giúp mk nhé
Tìm x biết : 2016^(2x-3).2016^4 = 2010.2016^4
Các bn giúp mk nhé
( 1.2 + 2.3 + 3.4 + ....... + 2012.2013) - ( 22 + 32 + 42 + 52 ........ + 20132 )
(1.2 + 2.3 + 3.4 + ... + 2012.2013) - (22 + 32 + 42 + 52 + ... + 20132)
= [(2 - 1).2 + (3 - 1).3 + (4 - 1).4 + ... + (2013 - 1).2013] - (22 + 32 + 42 + 52 + ... + 20132)
= (22 - 2 + 32 - 3 + 42 - 4 + ... + 20132 - 2013) - (22 + 32 + 42 + 52 + ... + 20132)
= 22 - 2 + 32 - 3 + 42 - 4 + ... + 20132 - 2013 - 22 - 32 - 42 - 52 - ... - 20132
= (22 - 22) + (32 - 32) + (42 - 42) + ... + (20132 - 20132) - (2 + 3 + 4 + ... + 2013)
= 0 - (2 + 3 + 4 + ... + 2013)
= 0 - (1 + 2 + 3 + 4 + ... + 2013) + 1
= 0 - \(\dfrac{2013.\left(2013+1\right)}{2}\) + 1
= 0 - 2027091 + 1
= (-2027091) + 1
= -2027090
Tìm số x thuộc Z, biết :
( x - 2 )2010 = ( x - 2 )2012
\(\left(x-2\right)^{2010}=\left(x-2\right)^{2012}\)
\(\Rightarrow\left(x-2\right)^{2010}-\left(x-2\right)^{2012}=0\)
\(\Rightarrow\left(x-2\right)^{2010}\left[1-\left(x-2\right)^2\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-2\right)^{2010}=0\\1-\left(x-2\right)^2=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x-2=0\\\left(x-2\right)^2=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x-2=\pm1\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=2\\x=3\\x=1\end{matrix}\right.\)
Cho A = 1.2.3.....100. Tìm số tự nhiên k lớn nhất để A chia hết cho 3k
Cho
A = 1.102 + 2.103 +3.104 + ........ + 299.400
B = 1^2 + 2^2 + 3^2 + .... + 299^2
Tính B - A