Prove that ∑ k=1
n
​
k(k+1)(k+2)= 4
n(n+1)(n+2)(n+3)
​
. 6. Show that ∑ k=1
n
​
k2 k
=(n−1)2 n+1
+2. 7. Suppose that you have 3 and 8 cent stamps, how much postage can you create using these stamps? Prove your conjecture using strong induction.