Ceiling and settling cracks can be very difficult to permanently fix. I have had a few. The only solution that worked for us was to have the crack cut out by about three to four feet on all sides and a sheet of drywall, I think you call it sheet rock, installed so there is no seam where the crack is. Usually cracks form where there is a seam. If a crack forms where there isn’t a seam, it could mean more than settlement. It is a messy job, but worth it. Needs to be done professionall.

Who did the engineering load calculations for the beam? Is it steel or what? The beam can't end above that doorway, so where is the end point? Where are both of the posts located that support the ends? Were new foundation piers poured for those posts? Have you been in the attic to measure the deflection of the beam itself?

IMO the house should have settled long a go if this is redo and removing a wall still requires support in the basement not just a jerry rigged beam where the wall was,

The person to call is a structural engineer. I very much suspect, either the beam is not adequate size, or that the under house (in basement? crawl space? supports are either lacking or insufficient.

My guess is that the beam that was put in was not of adequate size/strength. You are getting flexing and possible seasonal changes and the movement will prevent a simple, permanent repair. Short of opening up the ceiling and beefing up the beam, I can't think of what you can do that is aesthetically pleasing and will hide this problem. Sorry.

Regulars here know what I'm going to say -- that removing load bearing walls from houses designed by the architect to have them is expensive and complicated. It's not a DIY or handyman project, and requires design help from an experienced structural engineer (still more expense).

Open houses and walled houses are designed differently. Removing walls goes against your house's fundamental nature. If you decide that you want an open floor plan house, IMO you're usually better off selling your house designed to have walls, and buying one designed to be open.

That said, what's done is done, and I agree that you need to get a structural engineer in there stat. I can tell you from experience that you don't want to just cover the crack pictured. It almost certainly means trouble.

agree. if it's an older house, it's already settled. get an engineer out there to look at it. Have all the specs ready for him to review.

you have any pics of this beam being installed?