Sunday, September 9, 2018

real analysis - How to prove $B$ is the least possible upper bound?


I saw the following sequence-



$S_n=\frac12,\frac23,\frac34,\frac45,\frac56,\ldots,\frac{n-1}{n}$.





Now, I may say that-



$$ (A)\leq S_n\leq(B),$$



where, $A=\frac12$ and $B=1$



Now, am I correct in saying that $B$ is the least possible upper bound?



If yes, how do I prove it?




Thanks for any help.

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