how to Prove that the sequence an=(2n-1)/(n+1) converges to 2

Question : Prove that the sequence an=(2n-1)/(n+1) converges to 2 Solution: Given sequence \[a_n=\frac{2n-1}{n+1}\] The sequence an converges to a limit 2 if for every \(\epsilon\ > 0\) if there is an integer N such that \[\left|a_n-2\right|<\epsilon for all n\geq…

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