1\n(n+1)(n+2)(n+3)裂项

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1\n(n+1)(n+2)(n+3)裂项
如题,不要从网上上粘过来.

$1\n(n+1)(n+2)(n+3)裂项$

1/n(n+1)(n+2)(n+3)=1/[n(n+3)][(n+1)(n+2)]
=1/2[1/(n(n+3)--1/(n+1)(n+2)]
=1/2{1/3[(1/n--1/(n+3)]--[1/(n+1)--1/(n+2)]
=1/6(1/n)--1/6[1/(n+3)]--1/2[1/(n+1)]+1/2[1/(n+3)]
=1/6n--1/6(n--3)--1/2(n+1)+1/2(n+3).

证明不等式：(1/n)^n+(2/n)^n+(3/n)^n+.+(n/n)^n 2^n/n*(n+1) [3n(n+1)+n(n+1)(2n+1)]/6+n(n+2)化简化简(n+1)(n+2)(n+3) 计算：n(n+1)(n+2)(n+3)+1 lim[(n+3)/(n+1))]^(n-2) 【n无穷大】 (1/(n^2 n 1 ) 2/(n^2 n 2) 3/(n^2 n 3) ……n/(n^2 n n)) 当N越于无穷大当n为正偶数,求证n/(n-1)+n(n-2)/(n-1)(n-3)+...+n(n-2).2/(n-1)(n-3).. 1 + (n + 1) + n*(n + 1) + n*n + (n + 1) + 1 = 2n^2 + 3n + 3 化简：1/(n+1)(n+2)+1/(n+2)(n+3)+1/(n+3)(n+4) (n+1)(n+2)/1 +(n+2)(n+3)/1 +(n+3)(n+4)/1 证明(1+2/n)^n>5-2/n（n属于N+,n>=3)