Multiple choice

The sum of series $1.2 + 2.3 + 3.4 + ....10$ terms is

  1. $440$
  2. $286$
  3. $524$
  4. $\infty$
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A Correct answer
Explanation

The series is sum of n(n+1) for n=1 to 10. Sum = sum(n^2) + sum(n) = [n(n+1)(2n+1)/6] + [n(n+1)/2]. For n=10: (10*11*21/6) + (10*11/2) = 385 + 55 = 440.

AI explanation

The nth term of the given series can be written as n(n+1), which expands to n^2 + n. The sum to 10 terms is the sum of the first 10 natural squares plus the sum of the first 10 natural numbers. Using the standard sum formulas, the sum of squares is 10(11)(21)/6 = 385, and the sum of the first 10 integers is 10(11)/2 = 55. Adding these two sums together gives 385 + 55 = 440.

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