If \[{{x}_{n}}=\cos \,\left( \frac{\pi }{{{4}^{n}}} \right)+i\,\sin \,\left( \frac{\pi }{{{4}^{n}}} \right)\,,\] then \[{{x}_{1}}.\,{{x}_{2}}.\,{{x}_{3}}....\infty =\] [EAMCET 2002]

If \[{{x}_{n}}=\cos \,\left( \frac{\pi }{{{4}^{n}}} \right)+i\,\sin

1.	If \[{{x}_{n}}=\cos \,\left( \frac{\pi }{{{4}^{n}}} \right)+i\,\sin \,\left( \frac{\pi }{{{4}^{n}}} \right)\,,\] then \[{{x}_{1}}.\,{{x}_{2}}.\,{{x}_{3}}....\infty =\] [EAMCET 2002]
A.	\[\frac{1+i\sqrt{3}}{2}\]
B.	\[\frac{-1+i\sqrt{3}}{2}\]
C.	\[\frac{1-i\sqrt{3}}{2}\]
D.	\[\frac{-1-i\sqrt{3}}{2}\]
Answer» B. \[\frac{-1+i\sqrt{3}}{2}\]

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If \[{{x}_{n}}=\cos \,\left( \frac{\pi }{{{4}^{n}}} \right)+i\,\sin \,\left( \frac{\pi }{{{4}^{n}}} \right)\,,\] then \[{{x}_{1}}.\,{{x}_{2}}.\,{{x}_{3}}....\infty =\] [EAMCET 2002]

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