计算(7+1)(7^2+1)(7^4+1)(7^8+1)(7^16+1)
来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/09/25 03:20:23
计算(7+1)(7^2+1)(7^4+1)(7^8+1)(7^16+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
再问: 1/6是哪来滴?
再答: 因为前面乘了(7 - 1) ,也就是6,为了使等式的值不变,所以还要乘以 (1/6)
= (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
再问: 1/6是哪来滴?
再答: 因为前面乘了(7 - 1) ,也就是6,为了使等式的值不变,所以还要乘以 (1/6)
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