Question

大一高数第五题第七题求解。。

Answer 1

∵1/(1+2+3+...+k)=2/[k(k+1)] (k=1,2,3,.)
=2[1/k-1/(k+1)]
∴1/(1+2)=2(1/2-1/3)
1/(1+2+3)=2(1/3-1/4)
.
1/(1+2+3+.+n)=2[1/n-1/(n+1)]
故 lim(n->∞)[(1/(1+2)+1/(1+2+3)+.+1/(1+2+3+...+n)
=lim(n->∞){2(1/2-1/3)+2(1/3-1/4)+.+2[1/n-1/(n+1)]}
=lim(n->∞){2[1/2-1/(n+1)]}
=2(1/2-0)
=1.

请采纳下吧谢谢