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Calculus

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Use mathematical induction to prove that each proposition is valid for all positive integral values of n.

5^n + 3 is divisible by 4.

  • Calculus -

    5^0+3 = 4
    5^1 +3 = 8
    5^2+3 = 5*5^1 + 3 = 4*5^1 +5+3 =28
    5^3+3 = 5*5^2 + 3 = 4*25 + 5+3 = 128

    5^(n+1) + 3 = 5 * 5^n + 3
    = 4 *5^n + (5^n+3)
    ah ha
    4*5^n is divisible by 4 and so is (5^n+3)

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