Question

在线等好急的！！求大家帮忙解答一下这个数列题的第二问QAQ

Answer 1

Sn =(n^2+n)/2
n=1, a1=1
for n>=2
an = Sn -S(n-1)
2an = 2n
an =n

bn= 2^an + (-1)^n.an
let
dn = (-1)^n .an
Sn = d1+d2+...+dn
if n is even
Sn = 1-2 +3-4 +...+(n-1)-n
=-n/2
if n is odd
Sn = 1-2 +3-4 +...+(n-1)+n
= -(n-1)/2 + n
= (n+1)/2
ie
bn= 2^an + (-1)^n.an
= 2^n + (-1)^n. n
Tn = b1+b2+...+bn
Tn = 2(2^n -1) +(n+1)/2 , if n is odd
= 2(2^n -1) - (n/2) , if n is even