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algorithm for a sum

  • To: mathgroup at
  • Subject: [mg7648] algorithm for a sum
  • From: Xah Lee <xah at>
  • Date: Tue, 24 Jun 1997 03:36:11 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

I'm wondering if it is possible to to have a lower order algorithm for calculating the following sum. I have a non-negative integer sequence {f[1],f[2],...f[n]}. Suppose n=5,


I want the following sequence of sums:

resultA = Table[1+Sum[Product[li2[[j]],{j,1,i}],{i,1,n}],{n,1,Length at li2}];
ColumnForm at resultA

For speed, I have implemented the above formula as follows:

resultA = Rest at FoldList[#1+#2&,1,Rest@(FoldList[#1*#2&,1,li2])]

Is there a closed form to this formula? But if you have different implementation that's interesting, please post it too. Thanks.

 Xah, xah at,
 #1 author:

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