Question

设n为正整数，an表示1²+2²+……n²的和的个位数字，若n=1,2,3,4,5,6,7……求an的规律

不是有规律的数列

Answer 1

1^2的末尾数和11^2,21^2....111^2,121^2.......只要末尾是1的个位就是1
2^2的末尾数和22^2,12^2,32^2.....只要末尾是2的,个位就是4
3^2,13^2.................个位是9
4^2....................个位是6
5^2....................个位是5
6^2.....................个位是6
7^2........................个位是9
8^2........................个位是4
9^2.............................是1
10^2...............................是0
10个的和个位为5,20个个位即为0,所以20个一周期
规律:
an=1 n=1,21,41....(20k+1)
an=1+4=5 n=2,22,42....=20k+2(下依此类推)
an=4
an=0
an=5
an=1
an=0
4
5
5
1
0
4
5
5
6
0
9
5
0 n=20 40 60....=20k