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Giải:
Ta có:
2019.2020-1/2019.2020= 2019.2020/2019.2020 - 1/2019.2020
=1-1/2019.2020
Tương tự:
2020.2021-1/2020.2021= 1-1/2020.2021
Vì 1/2019.2020 > 1/2020.2021 nên -1/2019.2020 < -1/2020.2021
(vì là số nguyên âm)
⇒ 1-1/2019.2020 < 1-1/2020.2021
⇔ 2019.2020-1/2019.2020 < 2020.2021-1/2020.2021
Chúc bạn học tốt!
Ta có : \(\frac{2017.2018+1}{2017.2018}=1+\frac{1}{2017.2018}\)
\(\frac{2018.2019+1}{2018.2019}=1+\frac{1}{2018.2019}\)
Mà : \(\frac{1}{2017.2018}>\frac{1}{2018.2019}\) => \(\frac{2017.2018+1}{2017.2018}>\frac{2018.2019+1}{2018.2019}\)
\(\frac{2017.2018-1}{2017.2018}=1-\frac{1}{2017.2018}\)
\(\frac{2018.2019-1}{2018.2019}=1-\frac{1}{2018.2019}\)
Ta thấy \(2017.2018< 2018.2019\)
nên \(\frac{1}{2017.1018}>\frac{1}{2018.2019}\)
\(\Rightarrow\)\(1-\frac{1}{2017.2018}< 1-\frac{1}{2018.2019}\)
Vậy \(\frac{2017.2018-1}{2017.2018}< \frac{2018.2019-1}{2018.2019}\)
Vì 2016x2017-\(\frac{1}{2016x2017}\)=4066272
2017x2018-\(\frac{1}{2017x2018}\)=4070306
Mà 4066272<4070306
Nên a<b
Ta có:
\(C=\frac{2017.2018-1}{2017.2018}=1-\frac{1}{2017.2018}\)
\(D=\frac{2018.2019-1}{2018.2019}=1-\frac{1}{2018.2019}\)
Mà ta có:
\(\frac{1}{2017.2018}>\frac{1}{2018.2019}\Rightarrow1-\frac{1}{2017.2018}< 1-\frac{1}{2018.2019}\Rightarrow C< D\)
Bài làm :
Ta có :
\(x+2x+3x+...+2020x=2020.2021\)
\(\Leftrightarrow x\left(1+2+3+...+2020\right)=2020.2021\)
\(\Leftrightarrow x.\frac{\left(2020+1\right).2020}{2}=2021.2020\)
\(\Leftrightarrow x.\frac{2021.2020}{2}=2021.2020\)
\(\Leftrightarrow x=2\)
Vậy x=2
\(x+2x+3x+...+2020x=2020\cdot2021\)
\(x\left(1+2+3+...+2020\right)=2020\cdot2021\)
1 + 2 + 3 ... + 2020
Số số hạng :
\(\left(2020-1\right):1+1=2020\)
Tổng :
\(\left(2020+1\right)\cdot2020:2=2021\cdot1010\)
\(2021\cdot1010\cdot x=2020\cdot2021\)
\(1010x=2020\)
\(x=2\)