数列{an}中,a1=1,a(n+1)=1⼀2(a1+a2+a3.....+an),则{an}的前n项和Sn=?

2025-01-07 08:57:44
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回答1:

∵a(n+1) = S(n+1) - Sn
∴S(n+1) - Sn = 1/2Sn
∴S(n+1) = 3/2Sn
∴数列{Sn}是以S1 = a1 = 1为首项, 3/2为公比的对比数列。
∴Sn = 1×3/2^(n-1) = 3/2^(n-1)