n<n^2,(n+2)<(n+2)^2
n(n+2)<n^2(n+2)^2
即有
[(n+1)/n^2(n+2)^2]<[(n+1)/n(n+2)]
因
(n+1)/n(n+2=(1/n)-[1/(n+2)]
所以
[(n+1)/n^2(n+2)^2]<[(1/n)-1/(n+2)]
[(n+1)/n^2(n+2)^2]<[1-(1/3)+(1/2-1/4)+(1/3-1/5)+(1/4-1/6)+.....+(1/n)-1/(n+2)]]
=[1+1/2-1/(n+1)-1/(n+2)]
=(3n^2+9n-4)/(n^2+3n+2)
追问
这部写错了吧?
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