Bài 1:

  13/15 và 45/47                                                  35/65 và 17/47

= 1-13/15=2/15                                                =1-35/65=30/65

=1-45/47=2/47                                                 =1-17/47=30/47

-Vì 15<47 nên 2/15>2/47                                 -Vì 65>47 nên 30/65<30/47

Vậy 13/15>45/47                                            Vậy 35/65<17/47

Bài 2:

2/3 + 2/15 + 2/35 + 2/63 +...+2/101x103

=2/1x3+2/3x5+2/5x7+2/7x9+...+2/101x103

=1/1-1/3+1/3-1/5+...+1/101-1/103

=1/1-1/103=102/103

4/1x5 + 4/5x9 +...+ 4/101 x105

=1/1-1/5+1/5-1/9+...1/101-1/105

1/1-1/105=104/105

Bài `1:`

`a)` $\dfrac{13}{15}$ và $\dfrac{45}{47}$

Ta có:

`1-` $\dfrac{13}{15}$ `=` $\dfrac{2}{15}$

`1-` $\dfrac{45}{47}$ `=` $\dfrac{2}{47}$

Vì `15<47` nên $\dfrac{2}{15}$ `>` $\dfrac{2}{47}$

Hay $\dfrac{13}{15}$ `<` $\dfrac{45}{47}$

Vậy $\dfrac{13}{15}$ `<` $\dfrac{45}{47}$

`b)` $\dfrac{35}{65}$ và $\dfrac{17}{47}$

Ta có:

`1-` $\dfrac{35}{65}$ `=` $\dfrac{30}{65}$

`1-` $\dfrac{17}{47}$ `=` $\dfrac{30}{47}$

Vì `65>47` nên $\dfrac{30}{65}$ `<` $\dfrac{30}{47}$

Hay $\dfrac{35}{65}$ `>` $\dfrac{17}{47}$

Vậy $\dfrac{35}{65}$ `>` $\dfrac{17}{47}$

Bài `2:`

`a)` $\dfrac{2}{3}$ `+` $\dfrac{2}{15}$ `+` $\dfrac{2}{35}$ `+` $\dfrac{2}{63}$ `+...+` $\dfrac{2}{101×103}$

`=` $\dfrac{2}{1×3}$ `+` $\dfrac{2}{3×5}$ `+` $\dfrac{2}{5×7}$ `+` $\dfrac{2}{7×9}$ `+...+` $\dfrac{2}{101×103}$

`=` `1-` $\dfrac{1}{3}$ `+` $\dfrac{1}{3}$ `-` $\dfrac{1}{5}$ `+...+` $\dfrac{1}{101}$ `-` $\dfrac{1}{103}$

`=` `1-` $\dfrac{1}{103}$

`=` $\dfrac{102}{103}$

`b)` $\dfrac{4}{1×5}$ `+` $\dfrac{4}{5×9}$ `+...+` $\dfrac{4}{101×105}$

`=` `1-` $\dfrac{1}{5}$ `+` $\dfrac{1}{5}$ `-` $\dfrac{1}{9}$ `+...+` $\dfrac{1}{101}$ `-` $\dfrac{1}{105}$

`=` `1-` $\dfrac{1}{105}$

`=` $\dfrac{104}{105}$