allerySum of the first $n$ natural numbers, $1 + 2 + 3 + \ldots + n$, equals
A$n(n+1)/2$
B$n^2/2$
C$n!/2$
D$n(n+1)(2n+1)/6$
Answer & Solution
Correct answer: A. $n(n+1)/2$
1. This is an AP with first term $a = 1$, last term $l = n$, $n$ terms.
2. AP sum: $S_n = (n/2)(a + l) = (n/2)(1 + n) = \dfrac{n(n+1)}{2}$.
3. Examples: $1 + 2 + \ldots + 10 = 10 \cdot 11 / 2 = 55$ ✓; $1 + 2 + \ldots + 100 = 5050$ ✓.
4. Option B is approximate but wrong (missing the $/2$ for odd $n$ subtlety). Option C has no relation. Option D is the sum of SQUARES formula.
_Source: syllabus Mathematics, Ch 8, §8.5 (Sum of first $n$ natural numbers), p. 12._
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