Find this sum (1/2) - (1/√3) + (1/4) - (1/√5) + (1/6) - (1/√7) +...?

Update: I'll extend the expiration period a bit; this question generated so much interest, It would be very interesting if someone was able to show that the series in convergent!
Update 2: If I knew this question was going to get starred by 18 people, I would've asked this using my real profile (which I didn't because I thought this was a stupid question :] )

http://answers.yahoo.com/my/profile;_ylt=AtqNvAbFk2nVI.rBuQQwLhUCxgt.;_ylv=3?show=575ytZ48aa
9 answers 9