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The sum of the first 5 natural numbers is 15 or (5)(6)/2. The sum of the first 21 natural numbers is 231=(21)(22)/2, and the sum of the first 30 numbers is 465. Use inductive reasoning to derive the formula for the sum of the first n natural numbers.

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  1. sum of first 5 natural numbers = (5)(6)/2
    sum of first 21 natural numbers = (21)(22)/2
    sum of first 30 natural numbers = 465 = (30)(31)/2

    sum of first n natural numbers = (n)(n+1)/2 -- provable by induction

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