Sequence And Series Question 364
Question: If $ a_1,\ a_2,…………,a_{n} $ are in A.P. with common difference , $ d $ , then the sum of the following series is $ \sin d(\cos ec,a_1.cosec,a_2+cosec,a_2.cosec,a_3+……….. $ $ +cosec\ {a_{n-1}}cosec\ a_{n}) $
[RPET 2000]
Options:
A) $ \sec a_1-\sec a_{n} $
B) $ \cot a_1-\cot a_{n} $
C) $ \tan a_1-\tan a_{n} $
D) $ cosec\ a_1-cosec\ a_{n} $
Show Answer
Answer:
Correct Answer: B
Solution:
As given $ d=a_2-a_1=a_3-a_2=….=a_{n}-{a_{n-1}} $
$ \therefore $ $ \sin d,{cosec\ a_1cosec\ a_2+…..+cosec\ {a_{n-1}}cosec\ a_{n}} $ $ =\frac{\sin (a_2-a_1)}{\sin a_1.\ \sin a_2}+……+\frac{\sin (a_{n}-{a_{n-1}})}{\sin {a_{n-1}}\sin a_{n}} $ $ =(\cot a_1-\cot a_2)+(\cot a_2-\cot a_3)+…. $ $ +(\cot {a_{n-1}}-\cot a_{n}) $ $ =\cot a_1-\cot a_{n} $ .
BETA
