bn = a - 1/4
b = a - 1/4
a(n+1)=1/2*an,n為偶數(shù) 所以
a = a /2
a(n+1)=an+（1/4）,n為奇數(shù).所以
a = a + 1/4
轉(zhuǎn)化為
a = a - 1/4
所以 將
bn = a - 1/4
b = a - 1/4
均轉(zhuǎn)化為 a 的函數(shù)
bn = a - 1/2
b = a /2 - 1/4
所以
b/bn = 1/2
為等比數(shù)列
Sn = b1 * (1 - 1/2^n)/(1 - 1/2)
其中 b1 = a1 - 1/4 = a - 1/4
Sn = (2a - 1/2) (1 - 1/2^n)