prove by induction that the sum of first nth triangular numbers is the nth tetrahedral number for all n in z

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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?