A) 0
B) a
C) \[\sqrt{2}a\]
D) \[2a\]
Correct Answer: A
Solution :
We have \[\underset{n\to \infty }{\mathop{\lim }}\,\,\frac{{{S}_{n+1}}-{{S}_{n}}}{\sqrt{\sum\limits_{k=1}^{n}{k}}}=\underset{n\to \infty }{\mathop{\lim }}\,\,\frac{{{a}_{n+1}}}{\sqrt{\frac{n\,(n+1)}{2}}}=0\] (Since\[n\to \infty ,\,\text{numerator }\to a\text{ while}\,\,\text{denominator }\to \infty \text{)}\]
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