Ha ha ha, my sucky summation skills suck slightly less than simply sidestepping summation-solving. Let me explain: I had my only midterm last week in algorithms and I thought I did terribly, in part because of how I solved the following summation: . That summation came about when solving the recurrence T(n) = T(n-1) + 5^n-1, T(0)=2.

I haven’t had a calculus class or even a math class in a couple years, so I’ve forgotten a lot. I reasoned that 5ⁱ is much like i, so surely the solution would be much like this one. So I “solved” it as: . When I got out of the exam and talked it over with classmates, several said they had left the sum in sigma notation, not attempting to simplify it. I explained my process, feeling all smart, before getting shut down with “you can’t do that.” Oh, wait… Yeah, I guess you can’t.

However! Today, I was vindicated because while I did lose one point for my crappy summing skills, the others that left it in sigma notation lost three points for not trying. So solve those sums, students, and solve them shoddily! …All right, enough with the ‘s’ stuff.

Oh yeah, and I totally used Wolfram Alpha to generate the images above.