Cn=(n+1/n+2)+(n+2/n+1)证明:2n

问题描述:

Cn=(n+1/n+2)+(n+2/n+1)证明:2n

给不给分啊,这题太简单了.证明:Cn=(n+2-1/n+2)+(n+1+1/n+1)=2+[(1/n+1)-(1/n+2)]设Sn=C1+C2+.+Cn则:Sn=2n+(1/2-1/3+1/3-1/4+1/4-1/5.-1/n+2)=2n+(1/2-1/n+2)由于0小于(1/2-1/n+2)而(1/2-1/n+2)小于1/2所以2n...