Question

先观察下列等式，然后用你发现的规律解答问题。1/1*2=1-1/2 1/2*3=1/2-1/3 1/3*4=1/3-1/4...

若1/1*3+1/3*5+1/5*7+...+1/(2n)(2n+1)的值为17/35，求n的值

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/(2n-1)-1/(2n+1))
=1/2 (1-1/(2n+1))
=17/35
1-1/(2n+1)=34/35
1/(2n+1)=1/35
2n+1=35
2n=34
n=17

Answer 2

1/1*3+1/3*5+1/5*7+……+1/(2n-1)(2n+1)
=2(1-1/3+1/3-1/5+1/5-1/7+……+1/(2n)-1/(2n+1))
=1/2(1-1/(2n+1))
把17/35代入得：
1/2(1-1/(2n+1))=17/35
1-1/(2n+1)=34/35
1/(2n+1)=1/35
2n+1=35
n=17