Calculus/Summation

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Expert: - 11/8/2010


Question
Hello,

Can you please show me how the summation of sin(pi*j)/j, where j=-n to n equals pi?

Thank you

Answer
It is known that sin(πj) = 0 anytime j is an integer.
This means the summation is sin(πj)/j = 0 except where j = 0.

At the point  j=0, lim(x->0)(sin(x)/x) = 1.

I'm not sure what the π is there for, for the summation is really 1.

Calculus

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