已知数列{an}的通项公式为an=n*2^n,求该数列的前n项和Sn

2025-06-26 18:29:08
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回答1:

an= n*2^n = n* 2^(n+1) - n* 2^n = n* 2^(n+1) - ( n-1) * 2^n - 2^n
设 bn=2^n的前n项的和为Tn
Tn =2 (2^n-1)=2^(n+1) -2

Sn= n* 2^(n+1) -0 - Tn = n*2^(n+!) - 2^(n+1) +2
Sn = (n-1)*2^(n+1) + 2