n是自然数,求证1/(n+1)+1/(n+2)+1/(n+3)+·····+1/3n

n是自然数,求证1/(n+1)+1/(n+2)+1/(n+3)+·····+1/3n n是自然数,当n趋于无穷大时,求[n·tan(1/n)]^(n^2)的极限 证明不等式：(1/n)^n+(2/n)^n+(3/n)^n+.+(n/n)^n 已知888个连续正整数之和:n+(n+1)+(n+2)+(n+3)+(n+4)+(n+5)+(n+6)+(n+7)+·· 若n为自然数且n +1|1×2×3×…×n+ 1.求证：n +1是个质数 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).. n是自然数,0≤n≤101,则| n-1|+|n-2|+|n-3|+…+|n-100|的最小值, lim[n/(n^2+1^2)+n/(n2+2^2)+···n/(n^2+n^2)] n->无穷大 设n为自然数,求证1/(n+1)+1/(n+2)+1/(n+3)+...+1/(3n)>4n/(4n+1) 设n为自然数,求证n+1分之1+n+2分之1+n+3分之1+...+3n分之1大于4n+1分之4n 设f(n)=1+1/2+1/3+.+1/n 求证f(1)+f(2)+.+(n-1)=n·[f(n)-1]用数学归纳法 已知n是大于1的自然数,求证log n (n+1)>log n+1 (n+2)