∴ AP= 1/2AD= 1/2AF，∠APF=90，

∴∠AFP=30，

∴ PF= root 3×AP=6 root 3,

∴∠FAD=60，

∴ ∠DAE= 1/2∠FAD=30，

∴ AE=AD/cos30 =83cm，

(2)∫DP = 1/3AD = 4，

∴ AP=2/3AD=8

∴ FP= root ( 12？ 2-8? ) =4 yuan and 5 yuan,

∫ Germany = EF∠AED =∠AEF∠AED =∠FGE,

∴∠FGE=∠FEG，

∴EF=GF，

Let DE=x, then gf = X.

∫△APG∽△ADE，

∴ PG/DE=AP/AD，

∴pg = 2/3 times

∴2/3x+x = 4 ^ 5，

∴ x=( 12 root 5)/5,

∴ AE= root (AD？ +DE？ ) =( 12 root 30)/5;

(3)① by (2) AE= root (AD？ +DE？ ) =( 12 root 30)/5,

AE= 12 (2n/(2n- 1))，

② AE = 12 (2n/(2n- 1))，

∴ As n gets bigger and bigger, AE gets closer and closer to 12.

So, the answer is: 12. Is this it? Put your topic under Baidu.