数列{an}的前n项和Sn=n2+n+1;bn=(-1)nan(n∈N*);则数列{bn}的前50项和为( ) A.49 B.50 C.99 D.100
问题描述:
数列{an}的前n项和Sn=n2+n+1;bn=(-1)nan(n∈N*);则数列{bn}的前50项和为( )
A. 49
B. 50
C. 99
D. 100
答
∵数列{an}的前n项和Sn=n2+n+1,∴a1=s1=3,当n≥2时,an=Sn -sn-1=n2+n+1-[(n-1)2+(n-1)+1]=2n,故an=3 , n=12n , n≥2.∴bn=(-1)n an =− 3 , &...