求数列4,9,16,.,3n-1+2^n,.前n项的和Sn_数学解答

求数列4,9,16,.,3n-1+2^n,.前n项的和Sn

人气：345 ℃　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)