binomials approximated to arithmetic-geometric progression

 Below is the expression that approximates a binomial expression to arithmetic-geometric progression.

And here are the Wolfram screen shots for k=15 and a = 4000.

The LHS

The RHS

Thanks to Wolfram Alpha a million times. You have been very kind and very helpful.

I believe these expressions are of body. Body can understand these and that is how we have our intelligence.

Have a nice day, dear readers !!