对于任意正整数n,证明3^n+2-2^n+2+3^n-2^n能被10整除
人气:227 ℃ 时间:2019-08-19 11:21:17
解答
3^(n+2) - 2^(n+2) + 3^n -2^n
=9*3^n+3^n-4*2^n-2^n
=10*3^n-5*2^n
=10*3^n-10*2^(n-1)
=10*[3^n-2^(n-1)]
所以对于任意正整数n,3^(n+2) - 2^(n+2) + 3^n -2^n能被10整除
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