b: I=-15+13=-2

\(A=\frac{10^8+2}{10^8-1}=\frac{10^8-1+3}{10^8-1}=1+\frac{3}{10^8-1}\)

\(B=\frac{10^8}{10^8-3}=\frac{10^8-3+3}{10^8-3}=1+\frac{3}{10^8-3}\)

Nhận thầy 10⁸ - 1 > 10⁸ - 3

=> \(\frac{3}{10^8-1}< \frac{3}{10^8-3}\)

=> \(1+\frac{3}{10^8-1}< \frac{3}{10^8-3}+1\)

=> A < B

b) 17C = \(\frac{17\left(17^{203}+1\right)}{17^{204}+1}=\frac{17^{204}+1+16}{17^{204}+1}=1+\frac{16}{17^{204}+1}\)

17D = \(\frac{17\left(17^{202}+1\right)}{17^{203}+1}=\frac{17^{203}+1+16}{17^{203}+1}=1+\frac{16}{17^{203}+1}\)

Nhận thầy 17²⁰³ + 1 < 17²⁰⁴ + 1

=> \(\frac{16}{17^{203}+1}>\frac{16}{17^{204}+1}\)

=> \(\frac{16}{17^{203}+1}+1>\frac{16}{17^{204}+1}+1\Rightarrow17C>17D\Rightarrow C>D\) 

2:

a: =4+3/8+5+2/3

=9+3/8+2/3

=216/24+9/24+16/24

=216/24+25/24

=241/24

b; =2+3/8+1+1/4+3+6/7

=6+3/8+1/4+6/7

=6+5/8+6/7

=419/56

c: \(=2+\dfrac{3}{8}-1-\dfrac{1}{4}+5+\dfrac{1}{3}\)

=6+3/8-1/4+1/3

=6+1/8+1/3

=6+11/24

=155/24

d: \(=3+\dfrac{5}{6}+6\cdot\dfrac{13}{6}\)

=3+13+5/6

=16+5/6

=101/6

e: =3+1/2+4+5/7-5-5/14

=3+4-5+1/2+5/7-5/14

=2+7/14+10/14-5/14

=2+12/14

=2+6/7=20/7

f: =9/2+1/2:11/2

=9/2+1/11

=99/22+2/22=101/22

\(83-\left(2x+8\right)=-203\)

=>\(\left(2x+8\right)=83+203\)

=>\(2x+8=286\)

=>\(2x=278\)

=>\(x=\frac{278}{2}=139\)

83-(2x+8)=-203

<=> 2x+8=83--203

<=> 2x+8=286

<=>2x=278

<=>x=139

KẾT QUẢ ĐÚNG 100% NHÉ ^^

S = 1.2 + 2.3 + 3.4 + ... + 39.40

3S = 1.2.3 + 2.3.3 + 3.4.3 + ... + 39.40.3

3S = 1.2.(3-0) + 2.3.(4-1) + ... + 39.40.(41-38)

3S = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 +...+ 39.40.41 - 38.39.40

3S = 39.40.41

S = 39.40.41 : 3

S = 21320

203:(x-10)=8

       x-10=203:8

       x-10=25,375

           x=25,375+10

           x=35,375

CHẮC CHẮN LÀ ĐÚNG NÊN NHỚ TICK CHO MK NHA

202^203<203^202

Ta có :

202²⁰³ = 8 242 408¹⁰¹ ( 1 )

203²⁰² = 42 209¹⁰¹       ( 2 )

Từ ( 1 ) và ( 2 ) suy ra 202²⁰³ < 203²⁰²