Sn=2^n+p
S(n-1)=2^(n-1)+p
an=Sn-S(n-1)=2^n - 2^(n-1) =2^(n-1)
a1=2^(1-1)=1
an=a1 * q^(n-1)=q^(n-1)=2^(n-1) ==> q=2
Sn=a1*(1-q^n)/(1-q)=2^n-1 = 2^n +p
==> p=-1
bn=log 2 an=n-1
Tn= b1^2-b2^2 + b3^2 - b4^2 + ...+ bn^2 * (-1)^(n+1)
n為偶數(shù)時b(n-1)^2 - bn^2 = 3-2n
b1^2 - b2^2= 3 - 2*2
b3^2 - b4^2= 3 - 2*3
...
b(n-1)^2 - bn^2 = 3-2*n
2 邊相加
Tn= 3*(n/2) - 2* (n/2) * (n+2)/2
=n(1-n)/2
n為奇數(shù)時
T(n+1)=n(1-n)/2 + b(n+1)^2
=n*(n+1)/2
Tn=(n-1)*((n-1)+1)/2
=n*(n-1)/2