Wednesday, 3 February 2016

calculus - Prove frac1n+1lelogleft(1+frac1nright)lefrac1n,forallnge1 if logx=intx1fracdtt,x>0




I know it is very simple but something is going amiss.




We can see here that log(1+1n)=n+1ndtt



if t[n,n+1], 1n+11t1n



I want to show that 1n+1n+1ndtt1n.



Can I straight infer that? If so what is the logic behind it? I was thinking of using Σni=1 and sandwiching n+1ndtt between. But confused !


Answer



ntn+1




1n+11t1n



n+1ndtn+1n+1ndttn+1ndtn
1n+1n+1ndtt1n


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