Article View: rec.puzzles
Article #2680Re: closed form for a sum (SPOILER)
From: Daniel A. Asimov
Date: Wed, 13 Jan 1993 02:31
Date: Wed, 13 Jan 1993 02:31
30 lines
1449 bytes
1449 bytes
In article <1iv1enINNnq6@master.cs.rose-hulman.edu> goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard) writes: > >Evaluate: > \infinity > ___ > \ sin(n)/n > /___ > n = 1 >The solution is nice. >-- >Bart Goddard |Behold, thy King cometh unto thee, >Math. Dept. Rose-Hulman Inst. of Tech. |meek, and sitting upon an ass, and >goddard@nextwork.rose-hulman.edu |a colt, the foal of an ass. The sum is (pi - 1)/2. (Sketch): Identify the sum as the imaginary part of sum (exp(in)/n). Consider sum (z^n/n) and e.g. by differentiating this, identify it with log(1/(1-z)). Now plug in exp(in) for z, take the imaginary part, and use the half-angle formula to see that it is (pi-1)/2. Dan Asimov Mail Stop T045-1 NASA Ames Research Center Moffett Field, CA 94035-1000 asimov@nas.nasa.gov (415) 604-4799
Technical Details
Message-ID:
<1993Jan13.023158.24029@nas.nasa.gov>Path:
arc1-ca.pugleaf.net!sparky!uunet!zaphod.mps.ohio-state.edu!howland.reston.ans.net!spool.mu.edu!agate!ames!data.nas.nasa.gov!wk223.nas.nasa.gov!asimovReferences:
<1iv1enINNnq6@master.cs.rose-hulman.edu>Show Full Headers
Complete Article Headers
Newsgroups: rec.puzzles Path: arc1-ca.pugleaf.net!sparky!uunet!zaphod.mps.ohio-state.edu!howland.reston.ans.net!spool.mu.edu!agate!ames!data.nas.nasa.gov!wk223.nas.nasa.gov!asimov From: asimov@wk223.nas.nasa.gov (Daniel A. Asimov) Subject: Re: closed form for a sum (SPOILER) References: <1iv1enINNnq6@master.cs.rose-hulman.edu> Sender: news@nas.nasa.gov (News Administrator) Organization: NAS, NASA Ames Research Center, Moffett Field, California Date: Wed, 13 Jan 93 02:31:58 GMT Message-ID: <1993Jan13.023158.24029@nas.nasa.gov> Lines: 31