若n∈N+,求证√(1*2)+√(2*3)+...+√(n(n+1)

设n∈N,n>1.求证：logn (n+1)>log(n+1) (n+2) 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).. 证明不等式：(1/n)^n+(2/n)^n+(3/n)^n+.+(n/n)^n 若n∈N+，n≥2，求证：12−1n+1＜12 求证1/(n+1)+1/(n+2)+.+1/(3n+1)>1 [n属于N*] 正项级数(n-√n)/(2n-1)还有1/√n*ln(n+1/n-1)还有√(2n-1/3n+2)的敛散性 limn→∞n√(1+1/n)(1+2/n)...(1+n/n)等于多少? 求证:1+1/2+1/3+...+1/n>In(n+1)+n/2(n+1) (n属于N+) 数学定理证明求证2^n-1=2^n-1+2^n-2+2^n-3+.+2^n-n 求证c(n,1)+2c(n,2)+3c(n,3)+...+nc(n,n)=n2^(n-1) 2^n/n*(n+1) [3n(n+1)+n(n+1)(2n+1)]/6+n(n+2)化简