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Is \( \sum_{r=100}^{0} r \):

a) 5050

b) 0

c) -5050

d) other

I have an Opinion, but I don't want to share it until I know whether it's controversial (or worse yet, Wrong.)

@icecolbeveridge if you're going to say something about the empty set, I will fight you

@alephthought Thanks, Chris!

@topometallo Thanks!

@byorgey Thanks, Brent!

@icecolbeveridge Either (b) 0 or (d) -4950.

Case for (b): You're summing over all integers \(r\) such that \(100\le r\le 0\).

Case for (d): We want the identity \(\sum_{i=a}^b + \sum_{i=b+1}^c = \sum_{i=a}^c\) to hold for all \(a,b,c\). But notice the +1 in the second sum! So \( \sum_{r=0}^{99} r + \sum_{r=100}^{0} r = \sum_{r=0}^0 r = 0 \)

@icecolbeveridge But absolutely definitely not (a) or (c).

Christian Lawson-Perfect@christianp@mathstodon.xyz@icecolbeveridge a.