作业帮lim(n->∞){1/2*4+1/3*5+...+1/(n+1)(n+3)=?
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/21 18:57:36
lim(n->∞){1/2*4+1/3*5+...+1/(n+1)(n+3)=?
1/2*4=1/2(1/2-1/4)
1/3*5=1/2(1/3-1/5)
1/4*6=1/2(1/4-1/6)
1/(n+1)(n+3)=1/2[1/(n+1)-1/(n+3)]
lim(n->∞){1/2*4+1/3*5+...+1/(n+1)(n+3)=
lim(n->∞)1/2{1/2-1/4+1/3-1/5+1/4-1/6+ +1/(n+1)-1/(n+3)]
=lim(n->∞)1/2[1/2+1/3-1/(n+2)-1/(n+3)]=5/12
1/3*5=1/2(1/3-1/5)
1/4*6=1/2(1/4-1/6)
1/(n+1)(n+3)=1/2[1/(n+1)-1/(n+3)]
lim(n->∞){1/2*4+1/3*5+...+1/(n+1)(n+3)=
lim(n->∞)1/2{1/2-1/4+1/3-1/5+1/4-1/6+ +1/(n+1)-1/(n+3)]
=lim(n->∞)1/2[1/2+1/3-1/(n+2)-1/(n+3)]=5/12
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