May I ask what is the definition of Nilpotent matrix. I suppose that is A^k =0 for some k? If I am right, then 0 must be an eigenvalue of A, then there is some issues for the test problems.
@Ling Liang , take some tolerance while checking the equality of eigen value with zero.
Make a run-length companion vector
Do Fast Fourier Transformation
Create incrementing array
Sum of series VII
Sum of series III
Sum of series VI
Sum of series I
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