A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 4700 seats. The students
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Let
The exponent is indeed - not a typo!
Take the antiderivative of , denoted by
. This recovers a factor of
in the denominator, which lets us condense it to a single factorial.
Recall the series expansion of sine,
Then with a little algebraic manipulation, we get
Differentiate to recover .
Finally, , so our sum is