The sum of all roots of `sin(pi(log)_3(1/x))=0`in `(0,2pi)`is`3/2`(b) – InterviewSolution

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1.	The sum of all roots of `sin(pi(log)_3(1/x))=0`in `(0,2pi)`is`3/2`(b) 4(c) `9/2`(d) `(13)/3`A. `3//2`B. 4C. `9//2`D. `13//3`
Answer» Correct Answer - C `pi log_(3) (1/x)=k pi, k in I` `log_(3) (1/x)=k or x=3^(-k)` The possible values of k are `-1, 0, 1, 2, 3,...` `S=3+1+1/3+1/3^(2)+1/3^(3)+...oo=3/(1-1/3)=9/2`

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