已知数列{an}的前n项和Sn=n2+n2,n∈N*.(Ⅰ)求数列{an}的通项公式;(Ⅱ)设bn=2an+(-1)nan,求数列

2025-01-01 16:21:40
推荐回答(1个)
回答1:

(Ⅰ)当n=1时,a1=s1=1,
当n≥2时,an=sn-sn-1=

n2+n
2
-
(n?1)2+(n?1)
2
=n,
∴数列{an}的通项公式是an=n.
(Ⅱ)由(Ⅰ)知,bn=2n+(-1)nn,记数列{bn}的前2n项和为T2n,则
T2n=(21+22+…+22n)+(-1+2-3+4-…+2n)
=
2(1?22n)
1?2
+n=22n+1+n-2.
∴数列{bn}的前2n项和为22n+1+n-2.