A) \[\frac{{{2}^{n}}-1}{n}\]
B) \[\frac{{{2}^{n+1}}-1}{n+1}\]
C) \[\frac{{{2}^{n}}+1}{n}\]
D) \[\frac{{{2}^{n}}-1}{n+1}\]
Correct Answer: A
Solution :
[a] \[{{S}_{n}}=\frac{a({{r}^{n}}-1)}{r-1}=\frac{1.({{2}^{n}}-1)}{2-1}={{2}^{n}}-1\] Arithmatic Mean\[=\frac{({{2}^{n}}-1)}{2-1}\] Hence, option [a] is correct.
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