Question

已知数列{an}的前n项和为Sn=(-1)^n*n,则an=

Answer 1

a1=s1=-1

an=Sn-Sn-1

=(-1)^n*n-(-1)^(n-1)*(n-1)

(1)当n为奇数时,an=-n-(n-1)=-2n+1

(2)当n为偶数时,an=n+(n-1)=2n-1

所以：an=-2n+1,n=2k-1

an=2n-1,n=2k,(其中k∈N*)