(1)原式=1-
1
2 +
1
2 -
1
3 +
1
3 -
1
4 +
1
4 -
1
5 +
1
5 -
1
6 =1-
1
6 =
5
6 ;
(2)原式=1-
1
2 +
1
2 -
1
3 +
1
3 -
1
4 +
1
4 -
1
5 +…+
1
n -
1
n+1 =1-
1
n+1 =
n
n+1 ;
(3)
1
1×3 +
1
3×5 +
1
5×7 +…+
1
(2n-1)(2n+1)
=
1
2 (1-
1
3 )+
1
2 (
1
3 -
1
5 )+
1
2 (
1
5 -
1
7 ) +…+
1
2 (
1
2n-1 -
1
2n+1 )
=
1
2 (1-
1
2n+1 ) =
n
2n+1
由
n
2n+1 =
17
35 ,解得n=17,
经检验n=17是方程的根,
∴n=17.