Update one column as sum of other two columns

There's no need for loops or inner selects. Just try this:

UPDATE table1 SET column1 = column1 + column2

For all the rows you need not WHERE predicate:

UPDATE table SET
  column1 = column1+column2

thats all.

It's allowed to read from columns in the set clause:

UPDATE  table1 
SET     column1 = column1 + column2
WHERE   rowid = 1

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