ta có 

A/B=3^10+1/3^9+1 : 3^9+1/3^8+1

A/B=3^10+1/3^9+1 . 3^8+1/+3^9+1

A/B=(3^10+1).(3^8+1)/(3^9+1).(3^9+1)

A/B=3^18+3^10+3^8+1/3^18+3^9+3^9+1

Ta so sánh    3^10+3^8   và   3^9+3^9

                 3^8.(3^2+1)    và   3^8.(3+3)

                3^8.10             và    3^8.6

            vì   3^8.10  > 3^8.6

            nên  A>B

a= 1/2 + 1/4 + 1/8 - 1 x 1 + 8/1 - 4/1 - 2/1=\(1\frac{7}{8}\)=1,875

b=3/1 - 6/3 - 9/6 - 369/1 : 1/3 + 3/6 + 6/9 - 1/963 \(\approx\)186,665628245067

c=1/1 - 1/2 + 3/1 - 1/4 + 5/1 - 1/6 + 7/1 - 1/8 + 9/1 - 1/10=\(\approx\)23,8583333333333

                                     vậy a>b>c 

**************************l i k e***********************************8

A = \(\left(-\frac{1}{8}\right)\times\left(-13\right)=\frac{13}{8}\) => 0 < A < 2

B:  Tử âm ; mẫu dương => B < 0

C = \(\left(\frac{1}{1}+\frac{3}{1}+\frac{5}{1}+\frac{7}{1}+\frac{9}{1}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{10}\right)\)

= 25  \(-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{10}\right)\)

Dễ có: B < A < C 

bài 2

a, TS= 54 . 107 -53=(53+1) .107-53=53.107+107-53=53.107+ 54

<=> 

\(\frac{TS}{MS}\)=\(\frac{54.107+54}{54.107+54}\)=1

Bài 1 : 

\(a)\) Gọi \(ƯCLN\left(n+1;2n+3\right)=d\)

\(\Rightarrow\)\(\hept{\begin{cases}n+1⋮d\\2n+3⋮d\end{cases}\Rightarrow\hept{\begin{cases}2\left(n+1\right)⋮d\\2n+3⋮d\end{cases}\Rightarrow}\hept{\begin{cases}2n+2⋮d\\2n+3⋮d\end{cases}}}\)

\(\Rightarrow\)\(\left(2n+2\right)-\left(2n+3\right)⋮d\)

\(\Rightarrow\)\(2n+2-2n-3⋮d\)

\(\Rightarrow\)\(\left(-1\right)⋮d\)

\(\Rightarrow\)\(d\inƯ\left(-1\right)\)

Mà \(Ư\left(-1\right)=\left\{1;-1\right\}\)

\(\Rightarrow\)\(d\in\left\{1;-1\right\}\)

Do đó : 

\(ƯCLN\left(n+1;2n+3\right)=\left\{1;-1\right\}\)

Vậy \(\frac{n+1}{2n+3}\) là phân số tối giản với mọi n 

Chúc bạn học tốt ~ 

Bài 2 : 

\(a)\) Ta có : 

\(A=\frac{54.107-53}{53.107+54}=\frac{\left(53+1\right)107-53}{53.107+54}=\frac{53.107+107-53}{53.107+54}=\frac{53.107+54}{53.107+54}=1\)

\(B=\frac{135.269-133}{134.269+135}=\frac{\left(134+1\right)269-133}{134.269+135}=\frac{134.269+269-133}{134.269+135}=1+\frac{1}{134.269+135}>1\)

Vậy \(A< B\)

Chúc bạn học tốt ~ 

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

\(\frac{B}{3}=\frac{3^9+1}{3^9+3}=\frac{\left(3^9+3\right)-2}{3^9+3}=1-\frac{2}{3^9+3}\)

Vì \(3^{10}+3>3^9+3\) nên \(\frac{2}{3^{10}+3}< \frac{2}{3^9+3}\) \(\Leftrightarrow1-\frac{2}{3^{10}+3}>1-\frac{2}{3^9+3}\)

\(\Rightarrow\frac{A}{3}>\frac{B}{3}\) Hay \(A>B\)

Ta có:

\(A=\frac{3^{10}+1}{3^9+1}>\frac{3^{10}+3}{3^9+3}=\frac{3\left(3^9+1\right)}{3\left(3^8+1\right)}=\)\(\frac{3^9+1}{3^8+1}=B\Rightarrow A>B\)

\(A=\frac{3^{10}+1}{3^9+1}>1\Rightarrow A>\frac{3^{10}+1+2}{3^9+1+2}=\frac{3^{10}+3}{3^9+3}=\frac{3\left(3^9+1\right)}{3\left(3^8+1\right)}=\frac{3^9+1}{3^8+1}\)

??????????????????????????????????????????????????????????????????????????????????????

1/ Do A > 1 ; B < 1 nên A > B

2/ Áp dụng a/b > 1 <=> a/b < a+m/b+m ( a,b,m thuộc N*)

Do A > 1 nên A < 2015⁸ + 3 + 1 / 2015⁸ - 2 + 1 = 2015⁸ + 4 / 2015⁸ - 1 = B

=> A < B

1) Do A > 1 ; B < 1 nên A > B

2) Áp dụng a/b > 1 <=> a/b < a+m/b+m ( a,b,m thuộc N*)

Do A > 1 nên A < 2015⁸ + 3 + 1 / 2015⁸ - 2 + 1 = 2015⁸ + 4 / 2015⁸ - 1 = B

=> A < B

a.Vì \(\frac{17}{19}< 1\) và \(\frac{19}{17}>1\)

nên \(\frac{17}{19}< 1< \frac{19}{17}\)

hay \(\frac{17}{19}< \frac{19}{17}\)

b) \(\frac{15}{7}=2\frac{1}{7}\) và \(\frac{25}{12}=2\frac{1}{12}\)

Vì \(2\frac{1}{7}>2\frac{1}{12}\) nên \(\frac{15}{7}>\frac{25}{12}\)

\(A=\frac{54.107-53}{53.107+54}\)

\(\Leftrightarrow A=\frac{53.107+107-53}{53.107+54}\)

\(\Leftrightarrow A=\frac{53.107+54}{53.107+54}\)

\(\Leftrightarrow A=1\)

\(B=\frac{135.269-133}{134.269+135}\)

\(\Leftrightarrow B=\frac{134.269+269-133}{134.269+135}\)

\(\Leftrightarrow B=\frac{134.269+135}{134.269+135}\)

\(\Leftrightarrow B=1\)

Vì 1 = 1 nên A =B