If we use (x+) to indicate the following sum:
1 + 2 + 3 + ... + x
then find the value of k in the following equation:
(15+) - (14+) = (k+).


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Answer:

5

Step by Step Explanation:
  1. It is given that x+ = 1 + 2 + 3 + ... + x
  2. According to the question, (15+) - (14+) = (k+)
    ⇒ (1+2+3+ ... +15) - (1+2+3+ ... +14) = (1+2+3+ ... +k)
    ⇒ (1+2+3+ ... +14) + 15 - (1+2+3+ ... +14) = (1+2+3+ ... +k)
    ⇒ 15 = (1+2+3+...+k)
  3. Let us find the value of k for which sum of first k natural numbers is 15.
    Let us start with k = 2
    For k = 2, 1 + 2 = 3
    For k = 3, 1 + 2 + 3 = 6
    For k = 4, 1 + 2 + 3 + 4 = 10
    For k = 5, 1 + 2 + 3 + 4 + 5 = 15
  4. Hence, the value of k is 5.

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