Multiple choice

The sum of $10$ terms of the series $\sqrt{3}+\sqrt{12}+\sqrt{27}+\sqrt{48}+.....$ is:

  1. $55$
  2. $66$
  3. $45\sqrt{3}$
  4. $55\sqrt{3}$
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D Correct answer
Explanation

The series is sqrt(3) + 2*sqrt(3) + 3*sqrt(3) + 4*sqrt(3) + ..., which simplifies to sqrt(3) * (1 + 2 + 3 + ... + 10). The sum of the first 10 integers is (10 * 11) / 2 = 55. Thus, the total sum is 55*sqrt(3).

AI explanation

We simplify the terms by bringing the numbers outside the square roots to form the series 1 + 2 + 3 + ... + 10. The sum of this arithmetic progression is given by the formula n(n+1)/2, which evaluates to 10(11)/2 = 55. Multiplying this sum by the remaining square root gives the final sum of the 10 terms as 55*sqrt(3).

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