1. Use mathematical induction to prove the following equation is true for all integers n 2 1 . 1.2+2.22 + . . . + n . 2"=(n-1)2n+1 + 2 4. Chapter 4, Trees: Show that if any complete, balanced tree has three children at every node its depth k log, (2N + 1) where N is the total number of nodes in the tree including the root. (log , means log base three). Don't just show a few examples, show a math procedure, argument, or proof. Show all work, partial credit is given. Balance this tree (3g) Trees