(1+1/2)(1+1/2的2次方)(1+1/2的4次方)(1+1/2的8次方)+1/2的15次方.用平方差公式

假设s=(1+1/2)(1+1/4)(1+1/8)+1/2^15
两边同时乘以1-1/2
(1-1/2)s=(1-1/2)(1+1/2)(1+1/4)(1+1/8)+1/2*1/15
1/2s=(1-1/4)(1+1/4)(1+1/8)+1/16
1/2s=(1-1/8)(1+1/8)+1/16
1/2s=1-1/16+1/16
1/2s=1
s=2

(1+1/2)(1+1/2的2次方)(1+1/2的4次方)(1+1/2的8次方)+1/2的15次方
=（1-1/2）(1+1/2)(1+1/2的2次方)(1+1/2的4次方)(1+1/2的8次方)/（1-1/2）+1/2的15次方
=（1-1/2的2次方）(1+1/2的2次方)(1+1/2的4次方)(1+1/2的8次方)/（1-1/2）+1/2的15次方
=（1-1/2的4次方）(1+1/2的4次方)(1+1/2的8次方)/（1-1/2）+1/2的15次方
=（1-1/2的8次方)(1+1/2的8次方)/（1-1/2）+1/2的15次方
=(1-1/2的8次方)/(1+1/2的8次方)/（1/2）+1/2的15次方
=(1-1/2的16次方)*2+1/2的15次方
=2-1/2的15次方+1/2的15次方
=2.