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Find the sum of all possible products of the first `n` natural numbers taken two by two.
(a) `1/24 n(n + 1)(n - 1)(3n + 2)`
(b) `1/6 n(n + 1)(n - 1)(2n + 2)`
(c) `1/24 n(n - 1)(n + 1)(2n + 3)`
(d) none of these

Text Solution

AI Generated Solution

To find the sum of all possible products of the first `n` natural numbers taken two by two, we can follow these steps: ### Step 1: Understand the Problem We need to calculate the sum of the products of all combinations of two distinct natural numbers from the set {1, 2, 3, ..., n}. This can be represented mathematically as: \[ S = \sum_{1 \leq i < j \leq n} i \cdot j \] ...
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Knowledge Check

  • Find the sum of (1 - (1)/(n + 1)) + (1 - (2)/(n + 1)) + (1 - (3)/(n + 1))+......(1 - (n)/(n + 1))

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