求数列4,9,16,.,3n-1+2^n,.前n项的和Sn
人气:183 ℃ 时间:2020-03-20 03:56:47
解答
sn=3*1-1+2^1+3*2-1+2^2+.+3n-1+2^n
=3*(1+2+.+n)-n+2^1+2^2+.+2^n
=3n(n+1)/2-n+2*(1-2^n)/(1-2)
=(3n^2+3n-2n)/2+2*(2^n-1)
=(3n^2+n)/2+2^(n+1)-2
=(3n^2+n-4)/2+2^(n+1)
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