求证:n属于正整数,1/(n+1)+1/(n+2)~+1/2n>=2n/3n+1
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![求证:n属于正整数,1/(n+1)+1/(n+2)~+1/2n>=2n/3n+1](/uploads/image/z/11499981-69-1.jpg?t=%E6%B1%82%E8%AF%81%3An%E5%B1%9E%E4%BA%8E%E6%AD%A3%E6%95%B4%E6%95%B0%2C1%2F%28n%2B1%29%2B1%2F%28n%2B2%29%7E%2B1%2F2n%3E%3D2n%2F3n%2B1)
求证:n属于正整数,1/(n+1)+1/(n+2)~+1/2n>=2n/3n+1
求证:n属于正整数,1/(n+1)+1/(n+2)~+1/2n>=2n/3n+1
求证:n属于正整数,1/(n+1)+1/(n+2)~+1/2n>=2n/3n+1
用数学归纳法,当n=1时不等式成立.若结论对n成立,则有1/(n+2)+...+1/2n+1/2n+1+1/(2n+2)>=2n/(3n+1)+1/(2n+1)+1/(2n+2)-1/(n+1)=2n/(3n+1)+1/(2n+1)-1/(2n+2)=2n/(3n+1)+1/(2n+1)(2n+2)>(2n+2)/(3n+4),最后一个不等式是因为(倒推)1/(2n+1)(2n+2)>(2n+2)/(3n+4)-2n/(3n+1),等价于1/(2n+1)(2n+2)>2/(3n+4)(3n+1)等价于9n^2+15n+4>8n^2+12n+4