解:(1) 證明:由題意得

,
∴

········································································ 3分

又∵

∴


················································································ 4分
故

數列{b
n + 1}是以1為首項,2為公比的等比數列············································· 5分
(2) 由 (1) 可知,

,∴

·········································· 7分
故

················································ 9分
∴


············································ 10分
由

,得

∴滿足條件的n的最小值為10···································································· 12分