Question

猜想出n的n加1次方与的n次方的大小关系是怎样的

Answer 1

2^34^34^5>5^45^6>6^5------5>1.2^56^7>7^6-----6>(7/6)^6所设A=n^(n+1)>(n+1)^n=B求证C＝A=(n+1)^(n+2)>(n+2)^(n+1)=D则C/A/(n+1)=[(n+1)/n]^(n+1)=[1+1/n]^(n+1) D/B/(n+1)=[(n+2)/(n+1)]^(n+1)=[1+1/(n+1)]^(n+1)显然C/A > D/BC=C/A*A,是大数乘以大数因此所以C>D归纳,对所有n>2都成立：n的n+1次方　大于（n+1）的n次方