高数求极限问题设Xn=1+1/(1+2)+1/(1+2+3)+……+1/(1+2+3……+n)求lim n趋向于无穷 X
高数求极限问题
设Xn=1+1/(1+2)+1/(1+2+3)+……+1/(1+2+3……+n)求lim n趋向于无穷 Xn=
是用夹逼准则吗?如果是的话,怎么想呢?
设Xn=1+1/(1+2)+1/(1+2+3)+……+1/(1+2+3……+n)求lim n趋向于无穷 Xn=
是用夹逼准则吗?如果是的话,怎么想呢?
赞 驿路梨花处处开 幼苗
共回答了21个问题采纳率：90.5% 举报
Xn=1+
Xn=1+1/(1+2)+1/(1+2+3)+……+1/(1+2+3……+n)
=1+[1/3+1/6+1/10+……+1/（n(n+1)/2）]
=1+[2/(2*3)+2/(3*4)+2/(4*5)+……+2/(n(n+1))]
=1+2[1/(2*3)+1/(3*4)+1/(4*5)+……+1/(n(n+1))]
=1+2[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/n-1/(n+1))]
=1+2[1/2-1/3+1/3-1/4+1/4-1/5+……+1/n-1/(n+1)]
=1+2[1/2-1/(n+1)]
=1+2[1/2-0]
=1+1
=2
Xn=1+1/(1+2)+1/(1+2+3)+……+1/(1+2+3……+n)
=1+[1/3+1/6+1/10+……+1/（n(n+1)/2）]
=1+[2/(2*3)+2/(3*4)+2/(4*5)+……+2/(n(n+1))]
=1+2[1/(2*3)+1/(3*4)+1/(4*5)+……+1/(n(n+1))]
=1+2[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/n-1/(n+1))]
=1+2[1/2-1/3+1/3-1/4+1/4-1/5+……+1/n-1/(n+1)]
=1+2[1/2-1/(n+1)]
=1+2[1/2-0]
=1+1
=2
1年前
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