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Limit of a sum with parameters : Maple

I pretty novice with maple, I am working to compute a limit of a sum with maple but with two parameters.

I have

Sum(1/sqrt(k*n-sqrt(2)*n^2), k = sqrt(2)*n+1 .. (sqrt(2)+1)*n);

So then I do,

limit(1/sqrt(k*n-sqrt(2)*n^2), k = sqrt(2)*n+1 .. (sqrt(2)+1)*n, n = infinity);

And maple returned:

Error, invalid input: limit expects its 2nd argument, p, to be of type Or(name = algebraic, set(name = algebraic)), but received k = 2^(1/2)*n+1 .. (2^(1/2)+1)*n

How can I do to comput this limit ?

Thank you in advance for your time.

Solution

  • You forgot to include the Sum in the limit command.

    limit(Sum(1/sqrt(k*n-sqrt(2)*n^2), k= sqrt(2)*n+1 .. (sqrt(2)+1)*n), n= infinity);

    Maple responds:

                                      2