(a+1)(a2+1)(a4+1)(a8+1)(a16+1)=?_数学解答

(a+1)(a2+1)(a4+1)(a8+1)(a16+1)=?

人气：189 ℃　时间：2020-07-04 04:54:15

解答

(a+1)(a^2+1)(a^4+1)(a^8+1)(a^16+1)
=(a-1)[(a+1)(a^2+1)(a^4+1)(a^8+1)(a^16+1)]/(a-1)
=[a^2-1)(a^2+1)(a^4+1)(a^8+1)(a^16+1)]/(a-1)
=[(a^4-1)(a^4+1)(a^8+1)(a^16+1)]/(a-1)
=[(a^8-1)(a^8+1)(a^16+1)]/(a-1)
=[(a^16-1)(a^16+1)]/(a-1)
=(a^32-1)/(a-1)