Question

(1+1\2)(1+1\2平方)(1+\12的4次方)(1+1\2的8次方)+\12的15次方 怎么用平方差的公式计算啊

Answer 1

只要在乘积的前面引入2(1-1/2),就可以了.

(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15

=2(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15

=2(1-1/2^2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15

=2(1-1/2^4)(1+1/2^4)(1+1/2^8)+1/2^15

=2(1-1/2^8)(1+1/2^8)+1/2^15

=2(1-1/2^16)+1/2^15

=2-1/2^15+1/2^15

=2