aº+a¹+a²+a³计算公式 怎么推导出来的?
人气:249 ℃ 时间:2020-05-12 03:29:30
解答
原式=1+a³+a¹+a²
=(1+a)(a²-a+1)+a(1+a)
=(1+a)(a²+1)
=[(a+1)(a²+1)(a-1)]/(a-1)
=[(a²+1)(a²-1)]/(a-1)
=(a^4-1)/(a-1)
同理可推导出工a^n-1=(a-1)[aº+a¹+a²+a³……a^(n-1)]
即aº+a¹+a²+a³……a^(n-1)]=(a^n-1)/(a-1)
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