1+1/2+1/3+.+1/(2^n-1)>n/2
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1+1/2+1/3+.+1/(2^n-1)>n/2
用数学归纳法证明
用数学归纳法证明
当n=1时,不等式为1>1/2,成立.假设当n=k时,1+1/2+1/3+````+1/(2^k-1)>k/2成立 当n=k+1时,不等式为1+1/2+1/3+````+1/(2^k-1)+1/2^k+1/2^k+1```+1/2^(k+1)>k+1/2 因为 假设当n=k时,1+1/2+1/3+````+1/(2^k-1)>k/2成立 所以 1+1/2+1/3+````+1/(2^k-1)+1/2^k+1/2^k+1```+1/2^(k+1)>(k+1)/2可以化为 1/2^k+1/2^k+1```+1/2^(k+1)>1/2(只要证明这个成立即可) 运用放缩法左边1/2^k+1/2^k+1```+1/2^(k+1)>2^k(1/2^(k+1))>1/2,这样就证明出了.
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)