Think like Gauss. Gauss invented the formula for summing the first n integers by pairing up numbers. So, you paired up 1 with 48, 2 with 47, 3 with 46, and so on. Those sums are all the same: 1 + 48 = 49, 2 + 47 = 49, etc. How many of those pairs are there? n/2. Hence, (n/2)(n+1) is the sum. I bet you could reproduce this thinking for just the evens or just the odds. What do you think?