Mathematical induction (a) Prove that 5" – 1 1+5+...+5"-1 %3D 4 for all positive integers n. (b) Prove that 72n – 1 is divisible by 48 for all positive integers n. (c) Let T be a binary tree of height h > 1. Prove that T has at most 2h leaves.

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.