[15 pts] How Many Marks Until a Genie Appears? Weatherman Phil Connors has been stuck in a time loop on Groundhog Day, and needs your help to break the curse! He's been tracking how many days he's been stuck in the loop by marking a slip of paper (the paper doesn't reset after every day). On the first day, he puts 1 mark on the paper. The second day, he puts 2. This continues until the the nth day, for n 1. On the nth day, after drawing all n marks on the paper, a genie magically appears and tells Phil that he can be freed from the curse, but only if he can tell the genie how many marks he's drawn on his piece of paper without counting. As such, Phil needs to quickly find a closed form for the equation n i=1 i. Help save Phil and give a combinatorial proof for the following equation! n i=1 i = (n + 1 2 )