Get dates from a week number in T-SQL

Quassnoi's answer works, but kind of leaves you on the hook for cleaning up the dates if they are dates in the middle of the day (his start of week leaves you one day earlier than you need to be if you use a time in the middle of the day -- you can test using GETDATE()).

I've used something like this in the past:

SELECT 
   CONVERT(varchar(50), (DATEADD(dd, @@DATEFIRST - DATEPART(dw, DATECOL), DATECOL)), 101),
   CONVERT(varchar(50), (DATEADD(dd, @@DATEFIRST - DATEPART(dw, DATECOL) - 6, DATECOL)), 101)

A side benefit of this is that by using @@DATEFIRST you can handle nonstandard week starting days (the default is Sunday, but with SET @@DATEFIRST you can change this).

It seems crazy that simple date manipulation in SQL Server has to be this arcane, but there you go...

You can set @WeekNum and @YearNum to whatever you want - in this example they are derived from the @datecol variable, which is set to GETDATE() for purposes of illustration. Once you have those values- you can calculate the date range for a week by using the following:

DECLARE @datecol datetime = GETDATE();
DECLARE @WeekNum INT
      , @YearNum char(4);

SELECT @WeekNum = DATEPART(WK, @datecol)
     , @YearNum = CAST(DATEPART(YY, @datecol) AS CHAR(4));

-- once you have the @WeekNum and @YearNum set, the following calculates the date range.
SELECT DATEADD(wk, DATEDIFF(wk, 6, '1/1/' + @YearNum) + (@WeekNum-1), 6) AS StartOfWeek;
SELECT DATEADD(wk, DATEDIFF(wk, 5, '1/1/' + @YearNum) + (@WeekNum-1), 5) AS EndOfWeek;

To answer your question:

--CHANGE A WEEK NUMBER BACK INTO A DATE FOR THE FIRST DATE OF THE WEEK
DECLARE @TaskWeek INT = 17
DECLARE @TaskYear INT = 2013

SELECT DATEADD(WEEK, @TaskWeek - 1,DATEADD(dd, 1 - DATEPART(dw, '1/1/' + CONVERT(VARCHAR(4),@TaskYear)), '1/1/' + CONVERT(VARCHAR(4),@TaskYear)))