5^n+C（n,1）5^(n-1)+C（n,2）5^(n-2)+.+C（n,n-1）5 =(1+5)^n-1=6^n-1=(7-1)^-1
=7^n-C（n,1）7^(n-1)+C（n,2）7^(n-2)+.+(-1)^(n-1)*C（n,n-1）7+ (-1)^n-1
因上式中前n项之和为7的倍数,所以,当n为奇数时,被7除所得的余数是5；当n为偶数时,被7除所得的余数是0.