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RE: Re: Sum[n^(-n), {n, 1, Infinity}]

• To: mathgroup at smc.vnet.net
• Subject: [mg93351] RE: [mg93292] Re: Sum[n^(-n), {n, 1, Infinity}]
• From: "Tony Harker" <a.harker at ucl.ac.uk>
• Date: Tue, 4 Nov 2008 06:20:41 -0500 (EST)
• References: <gejiuo$2hf$1@smc.vnet.net> <200811031025.FAA05050@smc.vnet.net>

You get an interesting result if n has a value before you evaluate the
command:

  n=2
  Trace[Sum[n^(-n), {n, 1, Infinity}]]
  shows that what has been evaluated is the infinite sum of (1/4). 

 Could that be why some people have been getting Infinity?

  n=. 
  Trace[Sum[n^(-n), {n, 1, Infinity}]] 
  gives the unevaluated form.

  (Mathematica 6.0.3.0)

    Tony

Dr A.H. Harker
Department of Physics and Astronomy
University College London
Gower Street
London
WC1E 6BT

Tel: (44)(0) 2076793404
E:    a.harker at ucl.ac.uk

 EDUCATION, n. That which discloses to the wise and disguises from the
foolish their lack of understanding. (Ambrose Bierce, The Devil's
Dictionary, 1911)
 

]-> -----Original Message-----
]-> From: Helen Read [mailto:hpr at together.net] 
]-> Sent: 03 November 2008 10:25
]-> To: mathgroup at smc.vnet.net
]-> Subject: [mg93292] Re: Sum[n^(-n), {n, 1, Infinity}]
]-> 
]-> Jack Kennedy wrote:
]-> > Sum[n^(-n), {n, 1, Infinity}]
]-> > Surely this sum converges (~ 1.29).Mathematica 5.1 says 
]-> it's infinity.
]-> > What's going on?
]-> 
]-> Mathematica 6.0.3 spits it out unevaluated. NSum gives 1.29129
]-> 
]-> 
]-> --
]-> Helen Read
]-> University of Vermont
]-> 
]-> 

• References:
  • Re: Sum[n^(-n), {n, 1, Infinity}]
    • From: Helen Read <hpr@together.net>