Question

若S=A(1,1)+A(2,2)+A(3,3)+A(4,4)+.A(2009,2009),则S的个位数是

Answer 1

A(1,1)=1

A(2,2)=2

A(3,3)=6

A(4,4)=24

n≥5时,A(n,n)=A(5,5)*A(n,n-5)=A(n,n-5)*120, A(n,n)的个位数都是0

S=A(1,1)+A(2,2)+A(3,3)+A(4,4)+.A(2009,2009)

=1+2+6+24+120*[A(5,0)+A(6,1)+A(7,2)++.A(2009,2004)]

=120*[A(5,0)+A(6,1)+A(7,2)++.A(2009,2004)]+33

所以,S的个位数是3