Single Series (Levy's Method) for a Plate

Dear Mathcad Forum friends,

Im solving an exercise with Levy's method but in the end I'm having a discontinuity in the displacements of the plate. The problem is of this form:

The problem is that at the point y=1 i have a discontinuity and I dont even know where the problem is. . I will upload the file im working in, and also a file where i tried the load ti be continuous in y-direction, as in the following figure:

As always, i hope that any of you will be able to help me.

Maybe some knowledge in Civil Engineering is required in order to understand the problem. ,In case i have any mistake in the theory behind this solution, I am sorry for wasting your time.

Thank you in advance..