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 !!