I think it's really interesting that the triangular numbers are in the form (n + 1) C 2, and tetrahedral numbers are in the form (n + 2) C 3. In fact, the natural numbers are in the form n C 1. So, all these series can be defined as (n + r) C (r + 1), where r is any non negative integer!
@jbannon200 thanks for the reply, yes induction is pretty easy for this but I was more interested in a derivation, i was able to build a derivation geometrically but not purely algebraically. I'm more interested in finding out where the equations come from and what they relate to instead of simply proving that they just work.
I think it's really interesting that the triangular numbers are in the form (n + 1) C 2, and tetrahedral numbers are in the form (n + 2) C 3. In fact, the natural numbers are in the form n C 1. So, all these series can be defined as (n + r) C (r + 1), where r is any non negative integer!
EclecticSceptic 10 months ago
@jbannon200 thanks for the reply, yes induction is pretty easy for this but I was more interested in a derivation, i was able to build a derivation geometrically but not purely algebraically. I'm more interested in finding out where the equations come from and what they relate to instead of simply proving that they just work.
samruby82 11 months ago
@samruby82 @samruby82 nevermind, found a good one here: blog.jgc.org/2008/01/proof-that-sum-of-squares-of-first-n.html
samruby82 11 months ago
Do you ever end up proving the formula for square pyramidal numbers?
(n*(n-1)*(2n+1))/6.
Also, are you planning on showing the inductive proof, I'd be more interested in a derivation.
samruby82 11 months ago
the first table is just pascals triangle
mrsheetballz 1 year ago
Comment removed
hugstablebear 1 year ago