Question

若n为正整数,观察下列各式：1/1*3+1/3*5+1/5*7+………+1/（2n-1）（2n+1）=?

Answer 1

1/1*3+1/3*5+1/5*7+···+1/(2n-1)*(2n+1)

= 1/2 [1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ...+ 1/(2n-1) - 1/(2n+1)]

= 1/2 [1 - 1/(2n+ 1)]

= n/(2n + 1)