求极限Xn=1/(n^2+1)+2/(n^2+2)+3/(n^2+3)+……+n/(n^2+n)
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求极限Xn=1/(n^2+1)+2/(n^2+2)+3/(n^2+3)+……+n/(n^2+n)
求极限Xn=1/(n^2+1)+2/(n^2+2)+3/(n^2+3)+……+n/(n^2+n)
求极限Xn=1/(n^2+1)+2/(n^2+2)+3/(n^2+3)+……+n/(n^2+n)
k/(n^2+n)=
利用极限的夹逼准则来做:
k/(n^2+n)=
limXn<=1/2
Xn=∑k/(n^2+k) >=∑k/(n^2+n)=1/(n^2+n) *∑k=1/2
limXn>=1/2
夹逼定理做
xn>an=1/(n^2+n)+2/(n^2+n)+3/(n^2+n)+……+n/(n^2+n)xn
bn=1/2n(n+1)/n^2
lim an=1/2
lim bn=1/2
所以极限是1/2
n = 100000;
sum =0;
for (i=1;i
sum += i/((n*n)+i);
}
document.write(sum)
结果为:0.49999166674166906
所以极限是1/2
这么多人都答对了,我就不答了
1/2
k/(n^2+n)=
limXn<=1/2
Xn=∑k/(n^2+k) >=∑k/(n^2+n)=1/(n^2+n) *∑k=1/2
limXn>=1/2.
用积分做!!
Xn=∑k/(n^2+k) =∑1/(n*(n/k)+1) =
=(1/n)*∑1/(1/(k/n)+1/n)
因为n会趋于无穷大1/n就会很小取dx=1/n,k/n=x(k)
得积分为从0到1得积分 积分函数为1/{1/x +dx}=x
即x从0到1的积分 显然就为1/2
很多人做对了,看来不用我出手了~~~~~~~!