SOLUTION: Evaluate the limit of ({{{sin(pi/(3n)) + sin(2pi/(3n)) + sin(3pi/(3n))}}}+...+{{{ sin((n-2)pi/(3n)) + sin((n-1)pi/(3n))}}})/n as n goes to positive infinity (takes positive

Question 389814: Evaluate the limit of
(+...+)/n
as n goes to positive infinity (takes positive integer values.)
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
This is equivalent to finding the average y-value of from 0 to , since the x-values have equal density (the upper bound is because )

The average y-value is found by integrating the function, then dividing by the specified range (so that the average y-value times the domain will be equal to the definite integral). The area of from 0 to is

from to 0, which is . The domain is {0, pi/3} so the average value is
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