计算:已知M=(3+1)(3²+1)(3^4+1)(3^8+1),求2M+1的值
问题描述:
计算:已知M=(3+1)(3²+1)(3^4+1)(3^8+1),求2M+1的值
答
M=(3+1)(3²+1)(3^4+1)(3^8+1)
=(3-1)(3+1)(3²+1)(3^4+1)(3^8+1)/(3-1)
=(3²-1)(3²+1)(3^4+1)(3^8+1)/2
=(3^4-1)(3^4+1)(3^8+1)/2
=(3^8-1)(3^8+1)/2
=(3^16-1)/2
所以2M+1=3^16
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答
M=(3+1)(3²+1)(3^4+1)(3^8+1)=1/2(3-1)(3+1)(3²+1)(3^4+1)(3^8+1)=1/2(3²-1)(3²+1)(3^4+1)(3^8+1)=...=1/2*3^16-1/22M+1=2*(1/2*3^16-1/2)+1=3^16-1+1=3^16如追加其它问题,采纳本题后点击...