Summations arise regularly in mathematical analysis. For example,
Having a simple closed form expression such as makes the summation easier to understand and evaluate.
The summation we focus on in this post is
We will find a closed form for it.
In a recent post, I derived the closed form of a simpler summation (see “Beer theorems and their proofs“) Namely,
From (2) it follows that
which gives us
Let we arrived at (1)’s closed form:
I have a Computer Algebra aided solution too.
Therefore, the closed form of is the solution of initial-value problem
It is solved by Omega CAS Explorer (see Fig. 1)
At ACA 2017 in Jerusalem, I gave a talk on “Generating Power Summation Formulas using a Computer Algebra System“.
I had a dream that night. In the dream, I was taking a test.
Derive the closed form for
I woke up with a sweat.