1/6+1/12+1/20…+1/n(n+1)=

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1/6+1/12+1/20…+1/n(n+1)=
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1/6+1/12+1/20…+1/n(n+1)=
1/6+1/12+1/20…+1/n(n+1)=

1/6+1/12+1/20…+1/n(n+1)=
1/6+1/12+1/20…+1/n(n+1)=
=1/2×3＋1/3×4＋1/4×5＋...+1/n(n+1)
=1/2-1/3+1/3-1/4+1/4-1/5+...+1/n-1/(n+1)
=1/2-1/(n+1)
=(n-1)/[2(n+1)]

[3n(n+1)+n(n+1)(2n+1)]/6+n(n+2)化简 [3n(n+1)+n(n+1)(2n+1)]/6+n(n+2)化简 n^(n+1/n)/(n+1/n)^n 2^n/n*(n+1) 计算2+6+12+20+……+(n-1)n (n+1)^n-(n-1)^n=? 化简：(n+1)!/n!-n!/(n-1)! (n-1)*n!+(n-1)!*n 推导 n*n!=(n+1)!-n! 证明不等式：(1/n)^n+(2/n)^n+(3/n)^n+.+(n/n)^n 1/2+5/6+11/12+19/20+29/30+……+n平方-n-1/n(n-1) 用数学归纳法证明 6+2*9+3*12+…+n(3n+3)=n(n+1)(n+2) Sn=n(n+2)(n+4)的分项等于1/6[n(n+2)(n+4)(n+5)-(n-1)n(n+2)(n+4)]吗? 用数学归纳法证明：1*n+2(n-1)+3(n-2)+…+(n-1)*2+n*1=(1/6)n(n+1)(n+2) 根号（n+1)+n n.(n-1). (n+2)!/(n+1)! 判断 当n>1时,n*n*n>3n.( )