In the interval 0 , 2 π , sum of all the roots of the equation sin π log 3 1 x = 0 is

Step-by-step solution

π  log 3   1 x = k π ,  k ∈ I log 3   1 x = k   ⇒   x = 3 - k Possible values of k are –   1 ,   0 ,   1 ,   2 ,   3 ,   . . . . . . . S = 3 + 1 + 1 3 + 1 3 2 + 1 3 3 + ..... ∞ = 4 + 1 / 3 1 - 1 / 3 = 4 + 1 2 = 9 2