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已知3的一次方=3,3的平方=9,3的三次方=27,3的四次方=81,3的五次方=243,3的六次方=729……
A=2(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1 A的个位数字为( )
人气:470 ℃ 时间:2019-07-25 01:32:33
解答
个位数分别是3,9,7,1,3,9,7,1···
2(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)+1
={2[3+1)(3-1)](3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)+1}/(3-1)
={2[(3^2-1)(3^2+1)](3^4+1)(3^8+1)(3^16+1)(3^32+1)+1}/(3-1)
={2[(3^4-1)(3^4+1)](3^8+1)(3^16+1)(3^32+1)+1}/(3-1)
={2[(3^8-1)(3^8+1)](3^16+1)(3^32+1)+1}/(3-1)
={2[(3^16-1)(3^16+1)](3^32+1)+1}/(3-1)
={2[(3^32-1)(3^32+1)]+1}/(3-1)
={2(3^64-1)+1}/(3-1)
=(3^64-1)+1
=3^64
个位是1有什么不明白可以继续问,随时在线等.
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