摘要: [答案] 22.(Ⅰ) 设{an}的前n项和为Sn, 当q=1时, Sn=a1+a1+-+a1=na1; 当q≠1时, Sn=a1+a1q+a1q2+-+a1qn-1, ① qSn=a1q+a1q2+-+a1qn, ② ①-②得, (1-q) Sn=a1-a1qn, ∴Sn=, ∴Sn= (Ⅱ) 假设{an+1}是等比数列, 则对任意的k∈N+, (ak+1+1) 2=(ak+1) (ak+2+1), +2ak+1+1=akak+2+ak+ak+2+1, q2k+2a1qk=a1qk-1·a1qk+1+a1qk-1+a1qk+1, ∵a1≠0, ∴2qk=qk-1+qk+1. ∵q≠0, ∴q2-2q+1=0, ∴q=1, 这与已知矛盾. ∴假设不成立, 故{an+1}不是等比数列.

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