等差数列{an}的前n项和为Sn,若lim n→∞ Sn/n^2=2,则该数列的公差d=
A.4 B.2 C.-2 D.-4
人气:340 ℃ 时间:2020-03-23 03:37:41
解答
sn=a1n+n(n-1)d/2
所以
lim n→∞ Sn/n^2
=lim n→∞ 【a1n+n(n-1)d/2】/n^2=d/2=2
所以
d=4
选A【a1n+n(n-1)d/2】/n^2=d/2怎么来的? lim n→∞ 没有用吗?=lim n→∞ 【a1n+n(n-1)d/2】/n^2(分子分母同除以n²) =lim n→∞ 【a1/n+(1-1/n)d/2】 =0+(1-0)d/2 =d/2 =2 d=4
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