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+).
Answer:
5
- It is given that x+ = 1 + 2 + 3 + ... + x
- 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) - 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 - Hence, the value of k is 5.