Consider the five rows of numbers....
1 3/2 1
1 6/4 6/4 1
1 10/7 10/6 10/7 1
1 15/11 15/9 15/9 15/11 1
Let En(r) be the (r+1)th element in the nth row, starting with r=0. Example: E5(2) = 15/9
Find the General Statement for En(r).
Discuss the scope and limitations of the general statement.
I found the general statement by looking at the nth term of the numerators as this was dependent upon only n. I then found the difference between the num and dem in terms of n and r, so I could express it as a single term. It came to...
En(r) = (n^2+n)/(n^2+n-2rn+2r^2)
I believe this is correct. Nevertheless, I also need to find this general statement graphically and am uncertain of how to accomplish this. I would appreciate any suggestions.
I understand a limitation is that the general statement is valid only for
r<(or equal to) n. However, I have heard there are more limitations and would appreciate any suggestions.
Thank you in advance. (This is a more refined version of a question I previously posted, which received no responses. I have tried to make it more appealing this time.)