# Summing Deltas

Calculus Level 5

$\large \displaystyle \underset { n\rightarrow \infty }{ \lim } \frac { 1 }{ { n }^{ 2 } } \sum _{ k=1 }^{ n }{ { S }_{ k } }$

Let $${ S }_{ k }$$ denote area of triangle $${ AOB }_{ k }$$ with 2 given sides of $$OA=1$$, $${OB }_{ k }= k$$ and $$\angle {AOB }_{ k }=\dfrac { k\pi }{ 2n }$$ for positive integer $$k$$.

If the value of the limit above can be expressed as $$C\times \pi^D$$, where $$C$$ and $$D$$ are integers, find the value of $$C\times D$$.

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