C>D nhe em ei

2019 nhân 100 thì bằng 201900 > 20203

2020.2021 lớn hơn 100 suy ra b lớn hơn a

b<a

\(A=\dfrac{1}{2020}+\dfrac{1}{2020^2}+...+\dfrac{1}{2020^{2021}}\)

\(\Rightarrow2020A=1+\dfrac{1}{2020}+...+\dfrac{1}{2020^{2020}}\)

\(\Rightarrow2020A-A=\left(1+\dfrac{1}{2020}+...+\dfrac{1}{2020^{2020}}\right)-\left(\dfrac{1}{2020}+\dfrac{1}{2020^2}+...+\dfrac{1}{2020^{2021}}\right)\)

\(\Rightarrow2019A=1-\dfrac{1}{2020^{2021}}< 1\Rightarrow A< \dfrac{1}{2019}\)

\(131313-10101-20202=13\cdot10101-10101-2\cdot10101=10101\left(13-1-2\right)=10101\cdot10=101010\)

=10101x5/10101-10101x5/20202+10101x5/30303-10101x5/40404

=5-5/2+5/3-5/4

=35/12
 

cho đi

1. 

$=153^2+2.47.153+47^2=(153+47)^2=200^2=40000$

2.

$=1,24^2-2.1,24.0,24+0,24^2=(1,24-0,24)^2=1^2=1$

3. Không phù hợp để tính nhanh 

4. 

$=15^8-(15^8-1)=1$

5.

$=(1^2-2^2)+(3^2-4^2)+(5^2-6^2)+...+(2019^2-2020^2)$

$=(1-2)(1+2)+(3-4)(3+4)+(5-6)(5+6)+...+(2019-2020)(2019+2020)$

$=(-1)(1+2)+(-1)(3+4)+(-1)(5+6)+....+(-1)(2019+2020)$

$=(-1)(1+2+3+4+....+2019+2020)=(-1).2020(2020+1):2=-2041210$

6:

\(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)....\left(2^{2020}+1\right)+1\\ =1.\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)....\left(2^{2020}+1\right)+1\\ =\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)....\left(2^{2020}+1\right)+1\\ =\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)....\left(2^{2020}+1\right)+1\\ =\left(2^4-1\right)\left(2^4+1\right)....\left(2^{2020}+1\right)+1\\ =\left(2^8-1\right)....\left(2^{2020}+1\right)+1\\ =\left(2^{2020}-1\right)\left(2^{2020}+1\right)+1\\ =2^{4040}-1+1=2^{4040}\)

ta có :\(E=\frac{2019^{2019}+1}{2019^{2020}+1}\Leftrightarrow2019\cdot E=\frac{2019^{2020}+2019}{2019^{2020}+1}=1+\frac{2019}{2019^{2020}+1}\)

\(F=\frac{2019^{2020}+1}{2019^{2021}+1}\Leftrightarrow2019\cdot F=\frac{2019^{2021}+2019}{2019^{2021}+1}=1+\frac{2019}{2019^{2021}+1}\)

vì \(\frac{2019}{2019^{2020}+1}>\frac{2019}{2019^{2021}+1}\) nên E>F

E=2019 x 2019 x 2019 x ........ x 2019 x2019 +1 /2019 x 2019 x 2019 x.........x 2019 x 2019 + 1

E=1+1/2019+1

E=2/2020

E=1/1010

F=2019 x 2019 x 2019 x .......... x 2019 x 2019 +1 / 2019 x 2019 x 2019 x ....... x 2019 x 2019 +1

F= 1+1/2019+1

F=2/2020

F=1/1010

từ đó ta có E=F(=1/1010)

nghỉ sao rút gọn được vậy có dấu + mà(ví dụ\(\frac{2\cdot2+1}{2\cdot2\cdot2+1}=\frac{5}{9}\ne\frac{2}{3}\))

10101x(5/10101-5/20202+5/30303-5/40404)=10101x5/10101-10101x5/10101x2+10101x5/10101x3-10101x5/10101x4

                                                              =5-5/2+5/3-5/4

                                                              =35/12

k mk nha

a)( -26) +13+ 10+ 26

=(-26+26)+(13+10)

=0+23

=23

b)17+ 33+ ( -27)+ ( -33)

=[33+(-33)]+[17+(-27)]

=0+(-10)

=-10 

c)( -12) +( -250)+ (-8) +250 

=[-12+(-8)]+[-250+250]

=-20+0

=-20
d)( -19)+ ( -11) +31 +( -1)

=[-19+(-1)]+[-11+31]

=-20+20

=0 
e)(2019- 96)- 2019

=2019-96-2019

=(2019-2019)-96

=0-96

=-96

Bài 1. Tính nhanh các tổng sau
a) (-26) +13 + 10+ 26

= [(-26) + 26] + (13 + 10)

= 0 + 23

= 23
b) 17 + 33 + (-27) + (-33) 

= [17 + (-27)] + [33 + (-33)]

= -10 + 0

= -10
c) (-12) + (-250) + (-8) + 250 

= [(-12) + (-8)] + [(-250) + 250]

= -20 + 0

= -20
d) (-19) + (-11) + 31 +(-1) 

= [(-19) + (-11)] + [31 +(-1)]

= -30 + 30

= 0
e) (2019 - 96) - 2019

= 2019 - 96 - 2019

= (2019 - 2019) - 96

=0 - 96

#học tốt

&YOUTUBER&

a)(-26)+13+10+26

=[(-26)+26]+13+10

=0+13+10

=23

b)17+33+(-27)+(-33)

=[17+(-27)]+[33+(-33)]

=-10+0

=-10

c) (-12)+(-250)+(-8)+250

=(-12)+(-8)+[250+(-250)]

=(-12)+(-8)+0

=-20

d-19+11+31+-1

=(-19+-11)+(31+-1)

=-30+30

=0

e)(2019-96)-2019

=2019-96-2019

=2019-2019-96

=0-96

=-96