How would I calculate the sum or area of all the numbers in Pascal's Triangle stopping at row 111?
Would I refer to this as the sum? Or the area (A) within the triangle?
Also, how would I create a graphical image of Pascal's Triangle in Base 111? Like this Pascal's Triangle and how do I express a number that is within the row 111?
I have invested hours of research into these questions. The mathematical literature sends me in an infinite rabbit hole of confusion. I tend to struggle with basics.
Thank you for your knowledge if you've shared some with me.
Since the formula for calculating the sum of the numbers in row $n$ is $2^n$, the sum of all numbers up to a certain point is the sum of the first $n$ $2^n$ numbers, or in other case, $$2^{n+1} -1$$ In your case with the row being up to 111, the steps to answer this question is:
Step 1: Substitute $n$ with 111 $$2^{111+1} -1$$
Step 2: Use a calculator to calculate the expression because the product is very large.
The answer is $$5.192296858... * 10^{33}$$
Remember to calculate the "Area" of a pascal triangle up to base $n$ is $2^{n+1} -1$ :)