230问答网 > 计算(7+1)(7^2+1)(7^4+1)(7^8+1)(7^16+1)

计算(7+1)(7^2+1)(7^4+1)(7^8+1)(7^16+1)

2024-12-01 01:04:29

推荐回答（2个）

回答1：

(7 + 1)(7^2 + 1)(7^4 + 1)(7^8 + 1)(7^16 + 1)
= (1/6) × (7 - 1)(7 + 1)(7^2 + 1)(7^4 + 1)(7^8 + 1)(7^16 + 1)
= (1/6) × (7^2 - 1)(7^2 + 1)(7^4 + 1)(7^8 + 1)(7^16 + 1)
= (1/6) × (7^4 - 1)(7^4 + 1)(7^8 + 1)(7^16 + 1)
= (1/6) × (7^8 - 1)(7^8 + 1)(7^16 + 1)
= (1/6) × (7^16 - 1)(7^16 + 1)
= (1/6) × (7^32 - 1)
= (7^32 - 1)/6

回答2：

=(7+1)(7-1)(7^2+1)(7^4+1)(7^8+1)(7^16+1)/6
=(7^2+1)(7^2-1)(7^4+1)(7^8+1)(7^16+1)/6
=(7^4-1)(7^4+1)(7^8+1)(7^16+1)/6
=(7^8-1)(7^8+1)(7^16+1)/6
=(7^16-1)(7^16+1)/6
=(7^32-1)/6