已知31=3,32=9,33=27,34=81,35=243,36=729,37=2187,38=6561… 求(3-1)(3+1)(32+1)(34+1)•…•(332+1)+2的个位数字.
题目
已知31=3,32=9,33=27,34=81,35=243,36=729,37=2187,38=6561…
求(3-1)(3+1)(32+1)(34+1)•…•(332+1)+2的个位数字.
答案
原式=(3-1)(3+1)(32+1)(34+1)(38+1)(316+1)(332+1)+2
=(32-1)(32+1)(34+1)(38+1)(316+1)(332+1)+2
=(34-1)(34+1)(38+1)(316+1)(332+1)+2
=(38-1)(38+1)(316+1)(332+1)+2
=(316-1)(316+1)(332+1)+2
=(332-1)(332+1)+2
=364-1+2
=364+1,
64÷4=16,
所以364与34个位数字相同为1,
因此(3-1)(3+1)(32+1)(34+1)•…•(332+1)+2的个位数字是1+1=2.
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