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Show that 15^n cannot end with 0,2,4,6,8 for any natural no. |
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Answer» Step-by-step explanation: Let n = 1. 15^1 = 15, which ends with a 5. Suppose the HYPOTHESIS is true for n and consider n + 1. 15^(n + 1) = 15^n * 15 = p * 15 for some integer p that ends with a 5. Since the factors, p and 15, both end with a 5, their product, p * 15, will end with a 5. Therefore, 15^(n + 1) ends with a 5. Therefore, by induction, 15^(n + 1) ends with a 5 for all NATURAL NUMBERS, n. Therefore, 15^n can not end with the digit 0. |
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