prove by induction that the sum of first nth triangular numbers is the nth tetrahedral number for all n $\epsilon Z^+$
I know that by induction for triangular numbers we get
f(n) = 1+ 2+3....+n = n(n+1)\2
and if n =1 then we get 1(2)\ 2 = 1 true
we let n = k we get (k + 1)(k + 1 + 1)/2
im not sure how to tie this into tetrahedral numbers can someone explain?