otherwise, Examples on Mathematical induction: Trigonometry – principle of mathematical induction that T is the set of all integers greater than or equal to a; and so S is

Mathematical Induction Problems With Solutions. Question 1 : By the principle of mathematical induction, prove that, for n ≥ 1. 1 3 + 2 3 + 3 3 + · · · + n 3 = [n(n + 1)/2] 2. Solution : Let p(n) = 1 3 + 2 3 + 3 3 + · · · + n 3 = [n(n + 1)/2] 2. Step 1 :

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Use mathematical induction to prove that 1 + 2 + 3 + + n = n (n + 1) / 2 for all positive integers n. Solution to Problem 1: Let the statement P (n) be 1 + 2 + 3 + + n = n (n + 1) / 2 STEP 1: We first show that p (1) is true. Left Side = 1 Right Side = 1 (1 + 1) / 2 = 1 Both sides of the statement are equal hence p (1) is true. See more

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Here is a more reasonable use of mathematical induction: Show that, given any positive integer n n, n3 + 2n n 3 + 2 n yields an answer divisible by 3 3. So our property P P is: n3 + 2n n 3 + 2 n is divisible by 3 3. Go through the first two of