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MathGroup Archive 2007

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Re: HELP!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81192] Re: HELP!
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Sat, 15 Sep 2007 04:09:44 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <fcdfdj$pnr$1@smc.vnet.net>

conoverm at vt.edu wrote:

> How do i put a code in Mathematica 6.0 lab worksheet 2 of calculus I where I
> need to use sigma notation of (1/n!)
> I tried doing it but when i make a table it does not add the products of 1-3 if
> i put in as n goes to 3. Please help me with the code. Thank You
> 
> \[ExponentialE]=\!\(
> \*UnderoverscriptBox[\(\[Sum]\), \(n = 0\), \(\[Infinity]\)]
> \*FractionBox[\(1\), \(n!\)]\)=1+1/1!+1/2!+1/3!+1/4!+...

I am pretty sure I have not correctly understood what the problem is 
(i.e. typesetting or evaluating the sum expressed in sigma notation), 
but here are some examples that, I hope, will help your anyway. (They 
illustrate some of the feature of function such as Table, HoldForm, N, etc.)

In[1]:= Sum[1/n!, {n, 0, 3}]

Out[1]=
8
-
3

In[2]:= Plus @@ FoldList[1/HoldForm[#2]! &, 1, Range[5]]

Out[2]=
     1    1    1    1    1
1 + -- + -- + -- + -- + --
     1!   2!   3!   4!   5!

In[3]:= HoldForm@Sum[1/n!, {n, 0, 5}] ==
  Plus @@ FoldList[1/HoldForm[#2]! &, 1, Range[5]]

Out[3]=
     1                     1    1    1    1    1
Sum[--, {n, 0, 5}] == 1 + -- + -- + -- + -- + --
     n!                    1!   2!   3!   4!   5!

In[4]:= Limit[Sum[1/n!, {n, 0, x}], x -> Infinity]

Out[4]= E

In[5]:= Table[N@Sum[1/n!, {n, 0, x}], {x, 1, 5}]

Out[5]= {2., 2.5, 2.66667, 2.70833, 2.71667}

HTH,
-- 
Jean-Marc



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