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1、2015 18 232200 “ 、 ” 、 2015 18 2 1 1 n N * x n y = x 2n +2 +1 1 2 x 1 x n 2 T n = x 2 1 x 2 3 x 2 2n 1 T n 1 4n 2015 18 2 2 2 a n n S n n N * n S n y = b x +r b 0 b 1 b r 1 r 2 b =2 b n =2 log 2 a n +1 n N * n N * b 1 +1 b 1 b 2 +1 b 2 b n +1 b n n 槡 +1 2009 20 3 C n x 2 2 nx +y 2 =0 n =1 2 P 1 0 C
2、n k n k n 0 l n P n x n y n 1 x n y n 2 x 1 x 3 x 5 x 2n 1 1 x n 1 +x 槡 n 槡 2sin x n y n 2009 21 3 1 x n = n n +1 2 1 n 1 n =1 T 1 = x 2 1 = 1 4 T n 1 4n n = k T k 1 4k n = k +1 T k +1 = T k x 2 2k +1 1 4k 2k +1 2k ( ) +2 2 1 4k 2k +1 2k ( ) +2 2 1 4 k +1 = 1 16k k +1 2 0 6 4 2015 T k +1 1 4 k +1 n
3、= k +1 n N * T n 1 4n 2 n = k +1 2 、 2 a 1 a 2 a 3 a n = S n = 1 4n a 1 = 1 4 a n = S n S n 1 = n 1 n n 2 x 2 1 a 1 =0 x 2 2n 1 a n = 2n 1 2 ( ) n 2 n 1 n = 1 4n 2 0 n 2 x 2 2n 1 a n x 2 1 x 2 3 x 2 2n 1 a 1 a 2 a n = S n = 1 4n 、 3 3 n =1 T 1 = x 2 1 = 1 4 T n 1 4n n 2 A= 1 2 3 4 2n 1 2n B = 1 2 2
4、3 2n 2 2n 1 A B = 1 4n 2n 1 2n 2n 2 2n 1 A B T n = A 2 A B = 1 4n n N * T n 1 4n 4 、 4 T n 1 4n n T n 1 4 f n = n T n f n +1 f n = n +1 T n +1 n T n = n +1 x 2 2n +1 n = 4n 2 +4n +1 4n 2 +4n 1 f n +1 f n f n f n f 1 = 1 4 5 5 n =1 T 1 = x 2 1 = 1 4 T n 1 4n a 2 +1 2a a 2 2a 1 a =1 n 2 7 4 8 2015 18
5、x 2 3 2 x 3 1 = 1 2 x 2 5 2 x 5 1 = 2 3 x 2 2n 1 2 x 2n 1 1 = n 1 n T n 1 4 1 2 2 3 n 1 n = 1 4n n N * T n 1 4n 4 ( ) 1 2 2 ( ) 3 4 2 2n 1 2 ( ) n 2 1 4n 1 ( ) 1 2 1 ( ) 1 4 1 1 2 ( ) n 1 2 槡 n 1 a n a 1 1 d 1 a 1 d N * 1 1 a ( ) 1 1 1 a ( ) 2 1 1 a ( ) n a 1 1 a 1 a 1 a ( ) n 1 d T = 1 1 a ( ) 1 1 1 a ( ) 2 1 1 a ( ) n = a 1 1 a 1 a 2 1 a 2 a n 1 a n n =1 = a 1 1 a 1 = a 1 1 a 1 n 2 T = a 1 1 a 1 a 2 1 a 2
