2020 + 2018 x 9/ 2019 x 2020 - 2011=?
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Lời giải:
Số số hạng: $(2020-x):1+1=2021-x$
Giá trị tổng trên: $(2020+x)(2021-x):2=2020$
$(2020+x)(2021-x)=4040$
$2020.2021+x-x^2=4040$
$x^2-x+4040-2020.2021=0$
$x^2-x+2020(2-2021)=0$
$x^2-x-2019.2020=0$
$(x-2020)(x+2019)=0$
$\Rightarrow x=2020$ hoặc $x=-2019$
x=2020 nên x+1=2021
\(P\left(x\right)=x^{2021}-x^{2020}\left(x+1\right)+x^{2019}\left(x+1\right)-....+x\left(x+1\right)-2020\)
\(=x^{2021}-x^{2021}-x^{2020}+x^{2020}-...+x^2+x-2020\)
=x-2020=0
Ta có: \(2020=x\Rightarrow2019=x-1\)
Thay vào ta được:
\(D=x^{2020}+\left(x-1\right)^{2019}+\left(x-1\right)^{2018}+...+\left(x-1\right)x+1\)
\(D=x^{2020}+x^{2020}-x^{2019}+x^{2019}-x^{2018}+...+x^2-x+1\)
\(D=2x^{2020}-x+1\)
\(D=2\cdot2020^{2020}-2020+1\)
Bạn xem lại đề nhé
x = 2020 => 2019 = x - 1
Thế vào D ta được
D = x2020 + ( x - 1 )x2019 + ( x - 1 )x2018 + ... + ( x - 1 )x + 1
= x2020 + x2020 - x2019 + x2019 - x2018 + ... + x2 - x + 1
= 2x2020 - x + 1
= 2.20202020 - 2020 + 1
= 2.20202020 - 2019 ( chắc đề sai (: )
\(x=\frac{2019^{2020}+1}{2019^{2019}+1}>\frac{2019^{2020}+1+2018}{2019^{2019}+1+2018}=\frac{2019^{2020}+2019}{2019^{2019}+2019}=\frac{2019\left(2019^{2019}+1\right)}{2019\left(2019^{2018}+1\right)}=\frac{2019^{2019}+1}{2019^{2018}+1}\)(1)
\(y=\frac{2019^{2019}+2020}{2019^{2018}+2020}< \frac{2019^{2019}+2020-2019}{2019^{2018}+2020-2019}=\frac{2019^{2019}+1}{2019^{2018}+1}\left(2\right)\)
Từ (1) và (2) \(\Rightarrow x>y\)
2011+2012+2013+2014+2015+2016+2017+2018+2019+2020+2021+ 2022+2023 =(2011+2023)+(2013+2022)+...+(2016+2018)+2017 =4034+4034+4034+4034+4034+4034+2017 =4034x6+2017=26221
2011+2012+2013+2014+2015+2016+2017+2018+2019+2020+2021+2022+2023
=(2011+2023)+(2013+2022)+...+(2016+2018)+2017 =4034+4034+4034+4034+4034+4034+2017 =4034x6+2017=26221
\(\left(x+2018\right)^{2020}-\left(x+2018\right)^{2019}=0\)
\(\Leftrightarrow\) \(\left(x+2018\right)^{2019}\left(x+2018-1\right)=0\)
\(\Leftrightarrow\) \(\left(x+2018\right)^{2019}\left(x+2017\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x+2018\right)^{2019}=0\\x+2017=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2018\\x=-2017\end{matrix}\right.\)
\(\left(x+2018\right)^{2020}-\left(x+2018\right)^{2019}=0\\ \Leftrightarrow\left(x+2018\right)^{2019}\left[\left(x+2018\right)^2-1\right]=0\\ \Leftrightarrow\left(x+2018\right)^{2019}\left(x+2017\right)\left(x+2019\right)=0\\ \Rightarrow\left[{}\begin{matrix}x+2018=0\\x+2017=0\\x+2019=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-2018\\x=-2017\\x=-2019\end{matrix}\right.\)
1+2-3-4-5+6+7-8-9-10+11+12-13-14-15+...+2011+2012-2013-2014-2015+2016+2017-2018-2019-2020 giup mik v
Lời giải:
$A=(1+2-3-4-5)+(6+7-8-9-10)+(11+12-13-14-15)+....+(2011+2012-2013-2014-2015)+(2016+2017-2018-2019-2020)$
$=(-9)+(-14)+(-19)+....+(-2019)+(-2024)$
$=-(9+14+19+...+2019+2024)$
Số số hạng: $(2024-9):5+1=404$
$A=-(2024+9).404:2=-410666$
a)20182
b)4076369
18179,99554