Bài 1 :
A = $\dfrac{1}{3.5}$ + $\dfrac{1}{5.7}$ + $\dfrac{1}{7.9}$ + ....+$\dfrac{1}{37.39}$
=> A = $\dfrac{2}{2}$ . ( $\dfrac{1}{3.5}$ + $\dfrac{1}{5.7}$ + $\dfrac{1}{7.9}$ + ...+$\dfrac{1}{37.39}$ )
=> A = $\dfrac{1}{2}$ . ($\dfrac{2}{3.5}$ + $\dfrac{2}{5.7}$ + $\dfrac{2}{7.9}$ +...+$\dfrac{2}{37.39}$ )
=> A= $\dfrac{1}{2}$ . ( $\dfrac{1}{3}$ - $\dfrac{1}{5}$ + $\dfrac{1}{5}$ - $\dfrac{1}{7}$ + $\dfrac{1}{7}$- $\dfrac{1}{9}$ + ... + $\dfrac{1}{37}$ - $\dfrac{1}{39}$ )
=> A = $\dfrac{1}{2}$ . ( $\dfrac{1}{3}$ - $\dfrac{1}{39}$ )
=> A= $\dfrac{1}{2}$ . ( $\dfrac{13}{39}$ - $\dfrac{1}{39}$ )
=> A = $\dfrac{1}{2}$ . $\dfrac{12}{39}$ = $\dfrac{6}{39}$ = $\dfrac{2}{13}$
Vậy ....
Bài 2 :
B = $\dfrac{1}{3.4}$ + $\dfrac{1}{4.5}$ + $\dfrac{1}{5.6}$ +...+$\dfrac{1}{95.96}$
B = $\dfrac{1}{3}$ - $\dfrac{1}{4}$ + $\dfrac{1}{4}$ - $\dfrac{1}{5}$ + $\dfrac{1}{5}$ - $\dfrac{1}{6}$ + ...+ $\dfrac{1}{95}$ - $\dfrac{1}{96}$
B = $\dfrac{1}{3}$ - $\dfrac{1}{96}$
B = $\dfrac{31}{96}$
Bài 3 :
a) Để A là phân số thì n+2 phải khác 0 ( n ∈ Z )
=> n khác 0 -2
=> n khác (-2)
Vậy n khác (-2) để A là phân số
b) Để A là số nguyên thì 19 phải chia hết cho n+2
=> n+2 ∈ Ư(19)
=> n+2 ∈ { (-1) ; 1 ; (-19) ; 19 }
=> n ∈ { (-3) ; (-1) ; (-21) ; 17 }
Vậy ...
