Calculate Fourier Series coefficients using excel

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I am trying to calculate Fourier Series coefficients(a1 & b1) using formulae in excel for a particular case.

In a book by Henry Ludwell Moore, 'Economic Cycles :Their Law & Cause', the author has calculated these coefficients for rainfall data in Ohio valley. 

I am able to calculate them correctly for the cycles which divide the total data completely ( e.g. 8th cycle in 72 readings sample).

But I am unable to calculate for other cycles. (e.g. 10th cycle in 72 readings)

Please help.

I am unable to attach my worksheet and Moore's calculations for your kind reference.

 

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