![](https://rs.olm.vn/images/avt/0.png?1311)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có 1/2*2/3*...*2019/2020
=1*2*3*...*2019/2*3*4*..*2020
=1/2020 (rút gọn các số giống nhau)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ok em, để olm.vn giúp em nhá:
A = \(\dfrac{1}{2}\):3 + \(\dfrac{1}{3}\):4 + \(\dfrac{1}{4}\):5+...+\(\dfrac{1}{2018}\):2019 + \(\dfrac{1}{2019}\): 2020
A=\(\dfrac{1}{2}\times\dfrac{1}{3}+\dfrac{1}{3}\times\dfrac{1}{4}+\dfrac{1}{4}\times\dfrac{1}{5}+..+\dfrac{1}{2018}\times\dfrac{1}{2019}+\dfrac{1}{2019}\times\dfrac{1}{2020}\)
A = \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\)+....+ \(\dfrac{1}{2018}\) - \(\dfrac{1}{2019}\)+ \(\dfrac{1}{2019}\) - \(\dfrac{1}{2020}\)
A = \(\dfrac{1}{2}\) - \(\dfrac{1}{2020}\)
A = \(\dfrac{1009}{2020}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Số cần tìm là 5,32:0,125=42,56
b: \(A=1+\dfrac{1}{2019}-1-\dfrac{1}{2018}+\dfrac{1}{2018}-\dfrac{1}{2019}=0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{1x2}+\frac{1}{2x3}+...+\frac{1}{2018+2019}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2018}-\frac{1}{2019}\)
\(=1-\frac{1}{2019}\)
\(=\frac{2018}{2019}\)
\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2018.2019}\) ( đúng ko bn ?? )
= \(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2018}-\frac{1}{2019}\)
= \(\frac{1}{1}-\frac{1}{2019}=\frac{2018}{2019}\)
Học tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
Phân tích 2 phân số ta có:
1 = \(\dfrac{2017\times2019}{2017\times2019}\) = \(\dfrac{\left(2018-1\right)\times\left(2018+1\right)}{2017\times2019}\) = \(\dfrac{2018^2-1^2}{2017\times2019}\)
\(\dfrac{2018\times2018}{2017\times2019}\) = \(\dfrac{2018^2}{2017\times2019}\)
Vì \(2018^2\) > \(2018^2-1^2\) nên \(\dfrac{2018^2}{2017\times2019}\) > \(\dfrac{2018^2-1^2}{2017\times2019}\) hay \(\dfrac{2018\times2018}{2017\times2019}\) > 1
(Áp dụng hằng đẳng thức \(a^2-b^2\) = (a - b)(a + b))
nhầm dòng 2 nhé
\(=\dfrac{2018\times2018}{2018\times2018-1}=\)
Vì \(2018\times2018>2018\times2018-1\) nên \(\dfrac{2018\times2018}{2018\times2018-1}>1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\left(2020\times2019+2019\times2018\right)\times\left(1+\dfrac{1}{2}:1\dfrac{1}{2}-1\dfrac{1}{3}\right)\)
\(A=\left[2019\times\left(2020+2018\right)\right]\times\left(1+\dfrac{1}{2}:\dfrac{3}{2}-\dfrac{4}{3}\right)\)
\(A=4038\times2019\times\left(1+\dfrac{1}{3}-\dfrac{4}{3}\right)\)
\(A=4038\times2019\times0\)
\(A=0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\left(1+3+5+...+2019\right)-\left(2+4+...+2018\right)\\ =\dfrac{\left(2019+1\right)\left[\left(2019-1\right):2+1\right]}{2}-\dfrac{\left(2018+2\right)\left[\left(2018-2\right):2+1\right]}{2}\\ =\dfrac{1020100}{2}-\dfrac{1019090}{2}=505\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1) 2*17*9+18*540+29*18
= 18*17+18*540+29*18
= 18*(17+540+29)
= 18*586
= 10548
2) 5*{26-[3*(5+2*5)+15]/15}
= 5*{26-[3*(5+10)+15]/15}
= 5*{26-[3*15+15]/15}
= 5*{26-[45+15]/15}
= 5*{26-60/15}
= 5*{26-4}
=5*22
=110
3) (2018*2019+2019*2020)*(45*120-15*360)*(1+5+9+13+17+...+2015+2019)
= (2018*2019+2019*2020)*(15*3*120-15*120*3)*(1+5+9+13+17+...+2015+2019)
= (2018*2019+2019*2020)*0*(1+5+9+13+17+...+2015+2019)
= 0
Ta có:\(\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times..\times\frac{2018}{2019}\times\frac{2019}{2020}\)\(=\frac{1}{2020}\)
Vậy biểu thức \(\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times..\times\frac{2018}{2019}\times\frac{2019}{2020}\)\(=\frac{1}{2020}\)
1/2 x 2/3 x 3/4 x ... x 2018/2019 x 2019/2020
= 1 x 2 x 3 x ... x 2018 x 2019 / 2 x 3 x 4 x ... x 2019 x 2020
Khử loại đi ta còn lại phân số 1/2020
Hok tốt ^^