Foot Thumb

My three fingers and four fingers have resulted in many useful theories. Theories which are useful to not only technologists, engineers and technocrats but to scientists too. I do not want to list out the theories here as I want to focus on more important reason.

The thumb of the hands are better explained by slope of calculus theory. So I believe. If you are with me read further.

But what about the thumb of feet?

I believe the thumb of feet has a role as great as the thumb of hands. One does not realise but one can understand because there is symmetry in nature.

What could be the theory of thumb of feet?

At present I have two expressions. They are

While there is a pattern in the first expression; there is no such evident pattern in the second one. However Wolfram Alpha is able to dissect both the above expressions and is showing results.

I wish to state that I am not able to understand how 1) Wolfram Alpha solves the second expression 2) How to proceed in the second expression.

If I can be helped in any way please do. My thirst is quite high.

Or is the voice over internet is not heard? Or does it fall on deaf ears? Or is internet a dead media? Or you do not want to help?

I do not have clarity in this regard.