Problem 5.1. Prove 1+ ... +n = }n(n+ 1), that is, Ei = }n(n+1), for all natural i=1 numbers n by PMI (Principle of Mathematical Induction). Hint. Follow the steps (i), (ii) and (iii) as instructed. In the inductive step (ii), assume the statement is true when n = k for some natural number k, and then show the statement is k+1 true when n = k + 1. Note that ai = a + a2 + ·· · ak + ak+1 = + ak+1. ... i=1 i=1

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