已知3^1=3,3^2=9,3^3=27,3^4=81,3^5=243,3^6=729,3^7=2187,3^8=6561……求(3-1)(3+1)(3^2+1)
(3^4+1)……(3^32+1)+2的个位数字.
人气:163 ℃ 时间:2019-08-19 00:03:04
解答
解答﹙不断利用平方差公式﹚:
原式=﹙3²-1﹚﹙3²+1﹚……﹙3^32+1﹚+2
=﹙3^32-1﹚﹙3^32+1﹚+2
=3^64-1+2
=3^64+1
∵3^64的个位数=3^4个位数=1
∴原式的个位数字=2
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