Multiple choice

The sum of 20 terms of the series 1 + (1 + 3) + (1 + 3 + 5) + (1 + 3 + 5 + 7) +....is

  1. 400

  2. 2870

  3. 5740

  4. 1540
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B Correct answer
Explanation

The n-th term is the sum of the first n odd numbers, which is n^2. We need the sum of the first 20 terms: sum(n^2) from n=1 to 20. The formula is n(n+1)(2n+1)/6. For n=20: 20 * 21 * 41 / 6 = 2870.

AI explanation

The sum of the first n odd numbers is given by the formula n squared, so the terms of the series are the squares of natural numbers: 1, 4, 9, 16, and so on. We need to find the sum of the first 20 squares, which is calculated using the formula n(n + 1)(2n + 1) divided by 6. Substituting n = 20 gives (20 x 21 x 41) / 6, which equals 2870.

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