等差数列{an} 前n项和为sn,则lim(n趋向无穷)【sn/(an^2)】=?
人气:260 ℃ 时间:2020-02-05 15:26:56
解答
a(n)=a+(n-1)d,[a(n)]^2=[a+(n-1)d]^2=[nd+a-d]^2,
s(n)=na+n(n-1)d/2=(d/2)n^2+n(a-d/2),
当d=0时,a(n)=a,s(n)=na.
当d=0,a=0时,s(n)/[a(n)]^2没有意义.
当d=0,a不等于0时,s(n)/[a(n)]^2=n/a,lim(n->无穷大){s(n)/[a(n)]^2}=(n->无穷大){n/a}=正无穷大.
d不等于0时,
s(n)/[a(n)]^2=[(d/2)n^2+n(a-d/2)]/[nd+a-d]^2=[d/2+(a-d/2)/n]/[d+(a-d)/n]^2,
lim(n->无穷大){s(n)/[a(n)]^2}=lim(n->无穷大){[d/2+(a-d/2)/n]/[d+(a-d)/n]^2}=(d/2)/d^2=1/(2d)
推荐
- 设等差数列an的公差d为2,前n项和为Sn,则lim(an^2-n^2)/Sn=?
- 已知数列an是等差数列,且a1≠0,Sn为这个数列的前n项和.求1、lim nan/Sn 2、lim (Sn+Sn+1)/(Sn+Sn-1)
- 设等差数列{an}的公差d是2,前n项的和为Sn,则limn→∞a2n−n2Sn=_.
- 等差数列列{an}的前n项和为Sn,公差为2,则lim(n→∞)Sn/an^2=?
- 设等差数列的公差d为2,前n项和为Sn,则lim(n→∞)(an^2-n^2)/Sn
- Peole believe that the story is true 同义句
- 下列物质的化学式书写正确的是( ) A.氧化钠(NaO) B.氢氧化镁(MgOH) C.氯化锌(ZnCl2) D.碳酸钾(KCO3)
- 阴阳离子交换树脂的回收再利用方法,是已经不可以再生的,该怎样回收再利用?
猜你喜欢