If \[{{x}_{n}}=\frac{1-2+3-4+5-6+.....-2n}{\sqrt{{{n}^{2}}+1}+\sqrt{4{{n}^{2}}-1}},\] then \[\underset{n\to \infty }{\mathop{\lim }}\,{{x}_{n}}\] is equal to [AMU 2000]

If \[{{x}_{n}}=\frac{1-2+3-4+5-6+.....-2n}{\sqrt{{{n}^{2}}+1}+\sqrt{4{

1.	If \[{{x}_{n}}=\frac{1-2+3-4+5-6+.....-2n}{\sqrt{{{n}^{2}}+1}+\sqrt{4{{n}^{2}}-1}},\] then \[\underset{n\to \infty }{\mathop{\lim }}\,{{x}_{n}}\] is equal to [AMU 2000]
A.	\[\frac{1}{3}\]
B.	\[-\frac{2}{3}\]
C.	\[\frac{2}{3}\]
D.	1
Answer» C. \[\frac{2}{3}\]

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If \[{{x}_{n}}=\frac{1-2+3-4+5-6+.....-2n}{\sqrt{{{n}^{2}}+1}+\sqrt{4{{n}^{2}}-1}},\] then \[\underset{n\to \infty }{\mathop{\lim }}\,{{x}_{n}}\] is equal to [AMU 2000]

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