Bài 1: 

1: \(17A=\dfrac{17^{19}+17}{17^{19}+1}=1+\dfrac{16}{17^{19}+1}\)

\(17B=\dfrac{17^{18}+17}{17^{18}+1}=1+\dfrac{16}{17^{18}+1}\)

mà \(17^{19}+1>17^{18}+1\)

nên 17A>17B

hay A>B

2: \(C=\dfrac{98^{99}+98^{10}+1-98^{10}}{98^{89}+1}=98^{10}+\dfrac{1-98^{10}}{98^{89}+1}\)

\(D=\dfrac{98^{98}+98^{10}+1-98^{10}}{98^{88}+1}=98^{10}+\dfrac{1-98^{10}}{98^{88}+1}\)

mà \(98^{89}+1>98^{88}+1\)

nên C>D

S = 1 + 3 + 5 + 7 + ...+ 97 + 99

S = (1+99).[(99-1) : 2 + 1] : 2

S = 100.50 : 2

 S = 100.25

S = 2500

phần còn lại bn dựa vào mak lm nha\

Bài 2: tìm x 

a) 17.(x-13) = 17

x-13 = 1

x= 14

a, \(A=\frac{17^{18}+1}{17^{19}+1}< 1\)

\(A=\frac{17^{18}+1}{17^{19}+1}< \frac{17^{18}+1+16}{17^{19}+1+16}=\frac{17^{18}+17}{17^{19}+17}=\frac{17(17^{17}+1)}{17(17^{18}+1)}=B\)

\(\Rightarrow A< B\)

b, Tương tự câu a

a)Ta có : A =  \(\frac{17^{18}+1}{17^{19}+1}< \frac{17^{18}+1+16}{17^{19}+1+16}=\frac{17^{18}+17}{17^{19}+17}=\frac{17\left(17^{17}+1\right)}{17\left(17^{18}+1\right)}=\frac{17^{17}+1}{17^{18}+1}\)  = B

Vậy A < B

b) Làm tương tự như câu A

a: \(8\times427\times3+6\times573\times4\)

\(=24\times427+24\times573=24\times\left(427+573\right)\)

=24x1000

=24000

b: \(54\times47-47\times53-20-27\)

\(=47\times\left(54-53\right)-47\)

=47-47

=0

c: \(6\times1235\times20-5\times235\times24\)

=120x1235-235x120

=120x1000

=120000

d: \(\left(137\times99+137\right)-\left(17\times101-17\right)\)

\(=137\times\left(99+1\right)-17\times\left(101-1\right)\)

=137x100-17x100

=13700-1700

=12000

e: \(\left(145\times99+145\right)-\left(143\times101-143\right)\)

=145x(99+1)-143x(101-1)

=14500-14300

=200

g: \(\left(2003-123\times8:4\right)\times\left(36:6-6\right)\)

\(=\left(2003-123\times2\right)\times\left(6-6\right)\)

=0

b)Tận cùng=5 hoặc 0 nhưng mình ngại viết lắm,thông cảm nha

\(A=\frac{17^{18}+1}{17^{19}+1}< \frac{17^{18}+1+16}{17^{19}+1+16}\)

\(A=\frac{17^{18}+1}{17^{19}+1}< \frac{17^{18}+17}{17^{19}+17}\)

\(A=\frac{17^{18}+1}{17^{19}+1}< \frac{17^{17}+1}{17^{18}+1}=B\)

=> A < B

(98^99-1)/(98^98-1)

Sửa đề: \(C=\dfrac{17^{99}+1}{17^{99}-1}\)

\(C=\dfrac{17^{99}-1+2}{17^{99}-1}=1+\dfrac{2}{17^{99}-1}\)

\(D=\dfrac{17^{98}-1+2}{17^{98}-1}=1+\dfrac{2}{17^{98}-1}\)

17^99>17^98

=>17^99-1>17^98-1

=>C<D

\(x:x-54\cdot17\cdot\frac{6}{17}\cdot3\cdot4=12\)

\(x:x=12+\left(54\cdot17\cdot\frac{6}{17}\cdot3\cdot4\right)\)

x:x = ?

còn lại lm giúp mk nhá +0

1) Phân tích A ra :

 A= 17¹⁷.17+\(\frac{1}{17^{18}.17}\)+1 So sánh với B ta có: A có 17¹⁸>17¹⁷ của B nhưng B lại có 1/17¹⁸>1/17¹⁹.

Mà 17¹⁸>1/17¹⁸ nên suy ra A>B

2) Bài nay tương tự bài trên. 

2/(2012+2013) < 2/(2012 + 2012) = 2/ (2.2012) = 1/2012 
2009/(2012+2013) < 2009/2012 

=> 2011/(2012+2013) = 2/(2012+2013) + 2009/(2012+2013) < 1/2012 + 2009/2012 
=> 2011/(2012+2013) < 2010/2012 (a) 

2012/(2012+2013) < 2012/2013 (b) 

lấy (a) + (b) => (2011+2012)/(2012+2013) < 2010/2012 + 2012/2013 

vậy B < A