化简:(a-1)(1+1/a)(1+1/a^2)(1+1/a^4)(1+1/a^8)
问题描述：
化简:(a-1)(1+1/a)(1+1/a^2)(1+1/a^4)(1+1/a^8)
答
(a-1)(1+1/a)(1+1/a^2)(1+1/a^4)(1+1/a^8)
=(a-1)(1/a-1)(1/a+1)(1/a²+1)(1/a^4+1)(1/a^8+1)÷(1/a-1)
=(a-1)(1/a^2-1)(1/a^4-1)(1/a^8-1)÷(1/a-1)
=(a-1)((1/a^8-1)(1/a^8-+1)÷(1-a)/a
=(a-1)(1/a^16-1)*a/(1-a)
=a(1-1/a^16)
=a-1/a^15