设n为正整数根号n+4-根号n+3与根号n+2-根号n+1比大小

问题描述:

设n为正整数根号n+4-根号n+3与根号n+2-根号n+1比大小

因为(√n+4)+(√n+3)>(√n+2)+(√n+1),又(√n+4)-(√n+3)的平方差=(√n+2)-(√n+1)的平方差, 可算得(√n+4)-(√n+3)>(√n+2)-(√n+1)

根号n+4-根号n+3=1/[根号(N+4)+根号(N+3)]
根号n+2-根号n+1=1/[根号(N+2)+根号(N+1)]
由于:根号(N+4)+根号(N+3)>根号(N+2)+根号(N+1)
所以,根号n+4-根号n+3