计算:(2+1)(2*2+1)(2*4+1)……(2*2n+1).

问题描述:

计算:(2+1)(2*2+1)(2*4+1)……(2*2n+1).

(2+1)(2^2+1)(2^4+1)…(2^2n+1)
=(2-1)(2+1)(2^2+1)(2^4+1)…(2^2n+1)
=(2^2-1)(2^2+1)(2^4+1)…(2^2n+1)
=(2^4-1)(2^4+1)…(2^2n+1)
=(2^8-1)…(2^2n+1)
=...
=2^4n-1.