Sequence And Series Question 458
Question: What does the series $ 1+{3^{-\frac{1}{2}}}+3+\frac{1}{3\sqrt{3}}+… $ represents?
Options:
A) AP
B) GP
C) HP
D) None of the above series
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Given series is $ 1+\frac{1}{\sqrt{3}}+3+\frac{1}{3\sqrt{3}}+….. $ Consider $ \frac{a_2}{a_1}=\frac{1}{\sqrt{3}}, $ $ \frac{a_3}{a_2}=\frac{3}{1/\sqrt{3}}, $ $ \frac{a_4}{a_3}=\frac{1/3\sqrt{3}}{3} $ Also find $ a_2-a_1=\frac{1}{\sqrt{3}}-1=\frac{1-\sqrt{3}}{\sqrt{3}} $ $ a_3-a_2=3-\frac{1}{\sqrt{3}}=\frac{3\sqrt{3}-1}{\sqrt{3}} $ $ a_4-a_3=\frac{1}{3\sqrt{3}}-3=\frac{1-9\sqrt{3}}{3\sqrt{3}} $ Thus, $ \frac{a_2}{a_1}\ne \frac{a_3}{a_2}\ne \frac{a_4}{a_3} $ and $ a_2-a_1\ne a_3-a_2\ne a_4-a_3 $ Hence, given series is neither A.P, GP. nor HP.
BETA
