求(x+1)(x²+1)(x^4+1)(x^8+1)...(x^64+1)的值

问题描述:

求(x+1)(x²+1)(x^4+1)(x^8+1)...(x^64+1)的值

原式=(x-1)(x+1)(x²+1)(x^4+1)(x^8+1)...(x^64+1)/(x-1)
=(x²-1)(x²+1)(x^4+1)(x^8+1)...(x^64+1)/(x-1)
反复用平方差
=(x^128-1)/(x-1)