Discrete Structure20785 marksMathematical induction
Use mathematical induction to show that the sum of first n positive integers is n(n+1)/2.
Use mathematical induction to show that the sum of first n positive integers is n(n+1)/2. [5]
$$P(n): 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}{2}$$ for all positive integers $n \geq 1$. --- Left Hand Side (LHS): $$1$$ Right Hand Side (RHS): $$\frac{1(1+1)}{2} = \frac{1 \times 2}{2} = 1$$ Since LHS = RHS = 1, the statement P(1) is true. --- Assume that P(k) is true for some arbitrary positiv...