ta có: \(\frac{13}{38}>\frac{13}{39}=\frac{1}{3}=\frac{29}{87}>\frac{29}{88}\)

=> \(\frac{13}{88}>\frac{29}{88}\), mà đối với số âm, số nào dương lớn hơn thì nhỏ hơn

=> \(\frac{-13}{38}

b) \(\frac{-13}{38}< 1< \frac{29}{-88}\)

\(\frac{-13}{38}< \frac{29}{-88}\)

c)\(\frac{267}{-268}>1>\frac{-1347}{1343}\)

\(\frac{267}{-268}>\frac{-1343}{1343}\)

Bài này chỉ dùng cách so sánh với 1 là nhanh nhất 

\(b,-\frac{.13}{38}\)và \(\frac{19}{-88}\)

\(-\frac{13}{38}< 1< \frac{29}{-88}\)

\(\Rightarrow-\frac{13}{38}< \frac{29}{-88}\)

\(c,\frac{267}{-268}\)và \(-\frac{1347}{1343}\)

\(\frac{267}{-268}>1>-\frac{1347}{1343}\)

\(\frac{\Rightarrow267}{-268}>-\frac{1343}{1343}\)

Ta có: 1/3 = 13/39

=> 13/38 > 13/39 = 1/3

 1/3 = 29/87

=> 29/88 <29/87=1/3

 Vì 13/38 >1/3 > 29/88 nên -13/38 < -1/3 < -29/88

 Vậy -13/38 < -29/88

a,

\(-\frac{13}{38}=-1--\frac{25}{38}=-1+\frac{25}{38}\)

\(\frac{29}{-88}=-\frac{29}{88}=-1--\frac{59}{88}=-1+\frac{59}{88}\)

Vì \(\frac{25}{38}< \frac{59}{88}\Rightarrow-\frac{13}{38}< \frac{29}{-88}\)

b,

Ta có:

3³⁰¹ > 3³⁰⁰ = [3³]¹⁰⁰ = 27¹⁰⁰

5¹⁹⁹ < 5²⁰⁰ = [5²]¹⁰⁰ = 25¹⁰⁰

Mà 27¹⁰⁰ > 25¹⁰⁰ => 3³⁰¹ > 5¹⁹⁹

c,

\(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{\left[2n+1\right]\left[2n+3\right]}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2n+1}-\frac{1}{2n+3}\)

\(=1-\frac{1}{2n+3}< 1\)

Vậy P < 1

\(5^{199}=\left(5^{\frac{199}{301}}\right)^{301}\)

\(5^{\frac{199}{301}}< 3^1\)

\(\Leftrightarrow5^{199}< 3^{301}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2n+1}-\frac{1}{2n+3}\)

\(=1-\frac{1}{2n+3}< 1\)

Xét \(\frac{13}{38}>\frac{13}{39}=\frac{1}{3}=\frac{29}{87}>\frac{29}{88}\)

\(\Rightarrow\frac{13}{38}>\frac{29}{88}\)

\(\Rightarrow\frac{-13}{38}< \frac{29}{-88}\)

Vậy \(\frac{-13}{38}< \frac{29}{-88}\)

a, \(-\frac{13}{38}\) và \(\frac{29}{-88}\)

Ta có : 

\(\left(-13\right)\cdot\left(-88\right)=1144>29\cdot38=1102\)

b, Ta có :

\(-\frac{1}{5}< 0< \frac{1}{1000}\)

\(\Rightarrow\text{ }-\frac{1}{5}< \frac{1}{1000}\)