lim(2/2*3*4+2/3*4*5+...2/(n+1)(n+2)(n+3)) n→oo
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lim(2/2*3*4+2/3*4*5+...2/(n+1)(n+2)(n+3)) n→oo
![lim(2/2*3*4+2/3*4*5+...2/(n+1)(n+2)(n+3)) n→oo](/uploads/image/z/5597603-35-3.jpg?t=lim%282%2F2%2A3%2A4%2B2%2F3%2A4%2A5%2B...2%2F%28n%2B1%29%28n%2B2%29%28n%2B3%29%29+n%E2%86%92oo)
利用裂项,将2/((n+1)(n+2)(n+3))变成相减的形式,之后就可以前后项相互消除
具体步骤如下:
![](http://img.wesiedu.com/upload/d/fa/dfae5e1e3ae3d148bef4ed4dc75f2088.jpg)
具体步骤如下:
![](http://img.wesiedu.com/upload/d/fa/dfae5e1e3ae3d148bef4ed4dc75f2088.jpg)
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