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For each natural number, n( n + 1) is multiple of 2. |
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Answer» We have to prove that the product (n + 1) is divisible by 2. Now we have two cases. Either is even or odd. Let us examine each case. Suppose n is even. Then we can write n = 2 m, for same natural number m. And, then n(n + 1) = 2m (2m + 1) which is clearly divisible by 2. Next, suppose n is odd. Then n + 1 is even and we can write n + 1 = 2r, for some natural number 2. We have n(n + 1) = (2r - 1 2r = 2r (2r - 1) which is clearly divisible by 2. So, we can say that the natural number n(n + 1) is divisible by 2. |
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