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Re: Issue with Sum Version7

  • To: mathgroup at smc.vnet.net
  • Subject: [mg95637] Re: Issue with Sum Version7
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Fri, 23 Jan 2009 05:08:27 -0500 (EST)

On 1/22/09 at 7:05 AM, bghekaya at gmail.com wrote:

>Anyone seen this:

>In[120]:= Sum[i, {i, 0, 99999, .1}]

>Out[120]= 4.99991*10^10

>In[121]:= Sum[i, {i, 0, 100000, .1}]

>Out[121]= Sum[i, {i, 0, 100000, 0.1}]

>On Mac OS X 10.5.6

I get the same result. But this result is easily avoided by either

In[3]:= NSum[i, {i, 0, 100000, .1}]

Out[3]= 5.00001*10^10

or

In[4]:= Sum[i, {i, 0, 100000, 1/10}]

Out[4]= 50000050000

The general rule in Mathematica is when working with machine
precision numbers you should use the functions that start with N.

The key advantage of Sum over NSum is being able to return
symbolic answers for simple problems. Note

In[7]:= Sum[n, {n, 0, k, a}]

Out[7]= (k (a+k))/(2 a)

returns nearly instantly, much faster than doing the explicit sum.

Compare

In[1]:= Sum[n, {n, 0, 100000, 1/10}] // Timing

Out[1]= {0.135397,50000050000}

In[2]:= Sum[n, {n, 0, k, a}] /. {a -> 1/10, k -> 100000} // Timing

Out[2]= {0.018729,50000050000}

Of course none of this changes the fact there appears to be a
problem with Sum.



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