Given the following recursive definition is it possible to write it as a sum?

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- Mar 26th 2011, 02:35 PMdwsmithRecursive to Sum if possible
Given the following recursive definition is it possible to write it as a sum?

- Mar 26th 2011, 03:59 PMHallsofIvy
So ?

My suggestion would be to calculate some of them:

etc.

So it's clear that the formula involves . The powers on 1.03 are 0, 1, 1+ 2= 3, 1+ 2+ 3= 6, 1+ 2+ 3+ 4= 10, etc. for n= 1, 2, 3, 4, 5, ... That is, of course, .