special series

Question

The sum 1 + 2 + 3 + ... + n equals

RankGuru · Accepted Answer

1. **Identify the Series**: This is an AP with $a=1, d=1$, and last term $l=n$.
2. **Apply Sum Formula**: $S_n = \frac{n}{2}(a + l)$.
3. **Substitution**:
   - $S_n = \frac{n}{2}(1 + n) = \frac{n(n+1)}{2}$.
4. **Conclusion**: This gives the sum of the first $n$ natural numbers.

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