数列极限问题
问题描述：
数列极限问题
现在知道Sn=[(n+3)`n]/2
①求解1/S1+1/S2+```1/Sn的极限
答案是 11/9
②为什么1/Sn
答
Sn=[(n+3)n]/21/Sn=2/[n(n+3)]=(2/3)[1/n -1/(n+3)]1/S1+1/S2+...+1/Sn=(2/3)[1/1-1/4+1/2-1/5+...+1/n-1/(n+3)]=(2/3)[(1/1+1/2+...+1/n)-(1/4+1/5+...+1/(n+3))]=(2/3)[1+1/2+1/3 -1/(n+1)-1/(n+2)-1/(n+3)]=11/9 ...感谢！ 还有第二小题1/Sn011/9-(2/3)[1/(n+1)+1/(n+2)+1/(n+3)]