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Re: error with Sum and Infinity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg102274] Re: [mg102245] error with Sum and Infinity
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Mon, 3 Aug 2009 05:48:52 -0400 (EDT)
  • Reply-to: hanlonr at cox.net

$Version

7.0 for Mac OS X x86 (64-bit) (February 19, 2009)

t[i_] := 0

t[3] = 1

1

Sum[t[i], {i, 1, 10}]

1

Sum[t[i], {i, 1, Infinity}]

0

Check the summation by breaking the it into two segments: one with a finite number of terms and the other with an infinite number of terms. This appears to resolve the problem as long as the finite segment contains the specific value(s) and does not exceed about one million terms (version 7).

(Sum[t[i], {i, 1, #}] + Sum[t[i], {i, # + 1, Infinity}]) & /@
 
 Flatten[Table[{1, 2, 5} 10^n, {n, 0, 6}]]

{0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0}

Sum[t[i], {i, 1, 1000000}]

1

Sum[t[i], {i, 1, 1000001}]

0


Bob Hanlon

---- Llewlyn <tommaso.biancalani at gmail.com> wrote: 

=============
Hi experts,

i'm very new to Mathematica and this is my first problem. I define a
function that is 0 everywhere:
t[i_] := 0
expect for point i =3 that is:
 t[3] = 1
If now i evaluate the finite sum i obtain 1 as expected
Sum[ t[i], {i, 1, 10}]
Out = 1
but if i try do the same with infinity i obtain
In[808]:= Sum[ t[i], {i, 1, Infinity}]
Out[808]= 0
instead of 1 expected. Any advice?

tb




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