C1: ta có 8/9=1-1/9

              9/8=1+1/8

 Suy ra 9/8>8/9

C2: ta có 8/9=64/72<81/72=9/8

 tích nha

Cách 1 : 9/8 >1 ; 8/9 < 1 => 9/8 <8/9

Cách 2 : 9/8 = 72 / 64

8/9=64/64

=> 9/8 < 8/9

Đặt \(A=1+6+6^2+\cdots+6^9\)

=>\(6A=6+6^2+6^3+\cdots+6^{10}\)

=>6A-A=\(6+6^2+6^3+\cdots+6^{10}-1-6-6^2-\cdots-6^9\)

=>5A=\(6^{10}-1\)

=>\(A=\frac{6^{10}-1}{5}\)

\(P=\frac{6^{10}}{1+6+6^2+\cdots+6^9}\)

\(=\frac{6^{10}}{\frac{6^{10}-1}{5}}=\frac{5\cdot6^{10}}{6^{10}-1}=\frac{5\cdot6^{10}-5+5}{6^{10}-1}=5+\frac{5}{6^{10}-1}\)

=>P<6

\(B=1+8+8^2+\cdots+8^9\)

=>\(8B=8+8^2+\cdots+8^{10}\)

=>8B-B=\(8+8^2+\cdots+8^{10}-1-8-\cdots-8^9\)

=>7B=\(8^{10}-1\)

=>\(B=\frac{8^{10}-1}{7}\)

\(Q=\frac{8^{10}}{1+8+8^2+\cdots+8^9}\)

\(=8^{10}:\frac{8^{10}-1}{7}=\frac{8^{10}\cdot7}{8^{10}-1}=\frac{7\cdot8^{10}-7+7}{8^{10}-1}=7+\frac{7}{8^{10}-1}\)

=>Q>7>6

=>Q>P

a)Ta có:

 \(2^{94}\)

\(1024^9=\left(2^5\right)^9=2^{45}\)

\(2^{45}< 2^{94}\)

⇒\(2^{94}>1024^9\)

b) Ta có:

\(6^2+8^2=36+64=100\)

\(\left(6+8\right)^2=14^2=196\)

196>100

⇒\(6^2+8^2< \left(6+8\right)^2\)

2+2+2+...+2(100 lần)=2×100=200

8+8+8...+8(101 lần)=8×101=808

200<808 neen 2+2+2+...+2(100 lần) < 8+8+8+...+8(101 lần)

ta có : A=52

           B=9

=> A>B

TK MK NHÉ

CHÚC BN HỌC TỐT

Ta có :

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

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

Vì \(1+\dfrac{3}{10^8-1}< 1+\dfrac{3}{10^8-3}\Rightarrow A< B\)