(1)
Sn = (n^2+3n)/2
n=1 ,a1=2
an = Sn -S(n-1)
= (1/2)( 2n-1 + 3 )
= n+1
(2)
bn = an ; n is odd
= 2^n ; n is even
when n is even
Tn = b1+b2+...+bn
= [a1+a3+...+a(n-1)] + [2^2+2^4+...+2^n]
= (n+2)n/4+ (4/3)(2^n -1)
(3)
Tn - n^2/4 -24n =2008
(n+2)n/4+ (4/3)(2^n -1) -n^2/4 -24n =2008
-47n/2 + (4/3).2^n = 6028/3
8.2^n- 141n=12056
没有正整数n,可解以上方程式