a) \( 1+2+3+4+5+6 \)

Did you know that the sum of the first six positive integers, \(1 + 2 + 3 + 4 + 5 + 6\), is 21? This result can also be derived using the formula for the sum of an arithmetic series: \(S_n = \frac{n(n + 1)}{2}\). For \(n = 6\), it becomes \(S_6 = \frac{6(6 + 1)}{2} = 21\). Now, if you wanted to add up any longer sequences, this is just the tip of the iceberg! You can quickly find the sum of the first \(n\) integers using that formula, so whether you're summing to 100 or 1,000, it's a breeze. Just plug in the number into the formula and watch the magic happen!