integral problem with floor() function

Angsüsser shared this problem 3 years ago

I wanted to verify eulers summation formula, therefore I had to evalute the integral

Integral(f'(x) (x - floor(x)), 1, N)
f(x) is defined to 1/x; N is an integer-slider - as you can see by the attached worksheet.

Until N=9 the above integral evaluates correctly (unapproved!) - when the slider switches to 10 or greater the integral is undefined!

What happens here? Any idea or a bug in "integral"?

Comments (2)


creo que es un bug que tiene relación con la codificación de los numeros en el sistema binario porque es correcta para numeros del 1 al 9=2^3+1 y a partir de ahí para N=17,33,65 etc


Addition: Weird enough the above integral works for

N=(2^n + 1), n=3,4,5,6,.... -- for N= 9,17,33,65,

a workaround can be

-ln(N) + Sum(Integral(i / x², i, i + 1), i, 1, N - 1)

next I calculate the integral - and end up by doing all the work myself.

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