There's no need for a recursive CTE. If that query gives the correct results you can use it to update your table.

WITH CTE AS(

SELECT MTB.*,

Trail_Balance_Debit_New = MTB.ACTIVITYDEBIT + ISNULL(CTE.Trail_Balance_Debit, 0)

FROM #MyTrialBalance AS MTB

LEFT OUTER JOIN #MyTrialBalance CTE ON

MTB.Calendar_Month = DATEADD(month, 1, CTE.Calendar_Month)

)

UPDATE b SET

Trail_Balance_Debit = c.Trail_Balance_Debit_New

FROM #MyTrialBalance b

JOIN CTE c ON b.Trial_Balance_ID = c.Trial_Balance_ID

However, you could always try a fast method called Quirky Update (QU) which will help you to generate running totals. You can read more about it and other methods on the following article: http://www.sqlservercentral.com/articles/T-SQL/68467/

If you use the QU, be sure to follow all the rules.