1/(2.5)+1/(3.6)+....+1/(n+1)( n+4)+..
答案:1 悬赏:20 手机版
解决时间 2021-04-07 06:37
- 提问者网友：战魂
- 2021-04-06 23:55
1/(2.5)+1/(3.6)+....+1/(n+1)( n+4)+..
最佳答案
- 五星知识达人网友：街头电车
- 2021-04-07 00:26
1/(2×5)+ 1/(3×6)+...+1/[(n+1)(n+4)]
=⅓×[1/2 -1/5 +1/3 -1/6+...+1/(n+1) -1/(n+4)]
=⅓×[(1/2 +1/3+...+1/(n+1))-(1/5 +1/6+...+1/(n+4))]
=⅓×[1/2 +1/3 +1/4 -1/(n+2) -1/(n+3) -1/(n+4)]
=13/36-1/(3n+6) -1/(3n+9) -1/(3n+12)
lim1/(2×5)+ 1/(3×6)+...+1/[(n+1)(n+4)]
n→∞
=lim[13/36-1/(3n+6) -1/(3n+9) -1/(3n+12)]
n→∞
=13/36 -0 -0 -0
=13/36
=⅓×[1/2 -1/5 +1/3 -1/6+...+1/(n+1) -1/(n+4)]
=⅓×[(1/2 +1/3+...+1/(n+1))-(1/5 +1/6+...+1/(n+4))]
=⅓×[1/2 +1/3 +1/4 -1/(n+2) -1/(n+3) -1/(n+4)]
=13/36-1/(3n+6) -1/(3n+9) -1/(3n+12)
lim1/(2×5)+ 1/(3×6)+...+1/[(n+1)(n+4)]
n→∞
=lim[13/36-1/(3n+6) -1/(3n+9) -1/(3n+12)]
n→∞
=13/36 -0 -0 -0
=13/36
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