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ple 2.34Using mathematical induction method, Prove thatmin+1), nEN |
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Answer» Let the statement P (n) be1 + 2 + 3 + ... + n = n (n + 1) / 2STEP 1: We first show that p (1) is true.Left Side = 1Right Side = 1 (1 + 1) / 2 = 1Both sides of the statement are equal hence p (1) is true.STEP 2: We now assume that p (k) is true1 + 2 + 3 + ... + k = k (k + 1) / 2and show that p (k + 1) is true by adding k + 1 to both sides of the above statement1 + 2 + 3 + ... + k + (k + 1) = k (k + 1) / 2 + (k + 1)= (k + 1)(k / 2 + 1)= (k + 1)(k + 2) / 2The last statement may be written as1 + 2 + 3 + ... + k + (k + 1) = (k + 1)(k + 2) / 2Which is the statement p(k + 1) |
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