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Strange behavior of NSum on 4.0

• To: mathgroup at smc.vnet.net
• Subject: [mg28045] Strange behavior of NSum on 4.0
• From: Ken Kikuchi <kikuchi at neti.com>
• Date: Thu, 29 Mar 2001 03:24:11 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

I encountered a strange behavior with NSum on Mathematica 4.0 on Mac.
The following is a simplified example about sum of 1 to 25.

In[1]:= a = Range[25]
Out[1]=
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,
  15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}

In[2]:= NSum[a[[i]], {i, 25}]

I expected the result as 325 but received the following strange error
messages.

Part::pspec : 
    Part specification 41/2 is neither an integer nor a list of
integers.
...
NIntegrate::inum : 
    Integrand <<1>>[[41/2]] is not numerical at {1}={41/2}."

However, the same code works fine up to 24.
In[23]:= NSum[a[[i]], {i, 24}]
Out[23]= 300.

It works fine if not using Part.
In[3]:= NSum[i, {i, 25}]
Out[3]= 325.

But Part works fine with N while manual noted -- N[Sum[...]] calls NSum.
In[4]:= N[Sum[a[[i]], {i, 25}]]
Out[4]= 325.

And Sum works too.
In[5]:= Sum[a[[i]], {i, 25}]
Out[5]= 325

My version is,
In[6]:= $Version
Out[6]= "4.0 for Power Macintosh (July 26, 1999)"

I am not sure it's only my environmental problem or my incorrect usage.
Could anyone help me?

Many thanks,
Ken

• Follow-Ups:
  • Re: Strange behavior of NSum on 4.0
    • From: Tomas Garza <tgarza01@prodigy.net.mx>