阅读下题的解法:求3*5*17*……(2^2n-1+1)的值.原式=(2-1)(2+1)(2²+1)(2^4+1)……(2^2n+1)……=2^2n-1求(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)

问题描述:

阅读下题的解法:求3*5*17*……(2^2n-1+1)的值.
原式=(2-1)(2+1)(2²+1)(2^4+1)……(2^2n+1)
……
=2^2n-1
求(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)

(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)
=2×(1-1/2)×(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)
=2×(1-1/2^2)(1+1/2^2)(1+1/2^4)(1+1/2^8)
=2×(1-1/2^16)
=65535/32768;