Why MS Excel crashes and closes during Worksheet_Change Sub procedure?

I recommend this when using Worksheet_Change

1. You do not need the sheet name. In a Sheet Code Module, an unqualified Range reference refers to that sheet. That said, it is clearer to use the Me qualifier. If you are trying to use another sheet, then qualify the range reference with that sheet.

2. Whenever you are working with Worksheet_Change event, always switch Off events if you are writing data to any cell. This is required so that the code doesn't retrigger the Change event, and go into a possible endless loop

3. Whenever you are switching off events, use error handling to turn it back on, else if you get an error, the code will not run the next time.

Try this

Private Sub Worksheet_Change(ByVal Target As Range)
    On Error GoTo Whoa
    
    Application.EnableEvents = False
    
    Me.Range("A1:A8").Formula = "=B1+C1"
    
Letscontinue:
    Application.EnableEvents = True
    Exit Sub
Whoa:
    MsgBox Err.Description
    Resume Letscontinue
End Sub

Few other things that you may want to know when working with this event.

If you want to ensure that the code doesn't run when more than one cell is changed then add a small check

Private Sub Worksheet_Change(ByVal Target As Range)
    '~~> For Excel 2003
    If Target.Cells.Count > 1 Then Exit Sub
    
    '
    '~~> Rest of code
    '
End Sub

The CountLarge was introduced in Excel 2007 onward because Target.Cells.Count returns an Long value which can error out in Excel 2007 becuase of increased total cells count.

Private Sub Worksheet_Change(ByVal Target As Range)
    '~~> For Excel 2007
    If Target.Cells.CountLarge > 1 Then Exit Sub
    '
    '~~> Rest of code
    '
End Sub

To work with all the cells that were changed use this code

Private Sub Worksheet_Change(ByVal Target As Range)
    Dim aCell As Range
    
    For Each aCell In Target.Cells
        With aCell
            '~~> Do Something
        End With
    Next
End Sub

To detect change in a particular cell, use Intersect. For example, if a change happens in Cell A1, then the below code will fire

Private Sub Worksheet_Change(ByVal Target As Range)
    If Not Intersect(Target, Me.Range("A1")) Is Nothing Then
        MsgBox "Cell A1 was changed"
        '~~> Your code here
    End If
End Sub

To detect change in a particular set of range, use Intersect again. For example, if a change happens in range A1:A10, then the below code will fire

Private Sub Worksheet_Change(ByVal Target As Range)
    If Not Intersect(Target, Me.Range("A1:A10")) Is Nothing Then
        MsgBox "one or more Cells in A1:A10 range was changed"
        '~~> Your code here
    End If
End Sub

Excel was crashing, not the VBA function.
The events were not disabled and the call stack was filled by an infinite loop of OnChange events.
A little advice that helps finding this type of errors: set a breakpoint on the first line of the event, then execute it step by step pressing F8.