已知an前n项和sn=1/4n^2+2/3n,求an数列an中,an=2n-14,当n=多少时,sn取到最小值

Question

已知an前n项和sn=1/4n^2+2/3n,求an
数列an中,an=2n-14,当n=多少时,sn取到最小值

Answer 1

(1)
Sn=(1/4)n^2+(2/3)n
n=1, a1=11/12
for n>=2
an = Sn - S(n-1)
=(1/4)(2n-1) + 2/3
= (1/2)n + 5/12
(2)
an >0
2n -14 >0
n > 7
ie
a1,a2,...,a6