Math Contest #19 Results and Solution

Solution

The problem of this contest was to solve an infinite sum:

There are in general 3 different intuitive ways to find a solution to this:

1. 1-1+1-1+1-1+… = (1-1)+(1-1)+(1-1)+… = 0+0+0+… = 0
2. 1-1+1-1+1-1+… = 1 + (-1+1)+(-1+1)+(-1+1)+… = 1+0+0+0+… = 1
3. 1-1+1-1+1-1+… = x
   → 1-(1-1+1-1+1-1+…) = 1-x
   → 1-1+1-1+1-1+… = 1-x
   → x = 1-x
   → 2x = 1 → x = ½

But there are also infinitely many more ways to find a solution that you can explain. you could even reorder the sum(by taking some 1's from infinity and placing them between them at some point sooner in the sequence. This is possible, because before and after that operation the total number of 1's and -1's is still the same as before(∞)) to:
1+1-1+1+1-1+1+1-1+… = (1+1-1)+(1+1-1)+… = 1+1+1+… = ∞

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List of participants with their entries:

Name	solutions found	comment
@sparkesy43	0 or 1
@crokkon	0 or ½ or 1
@golddeck	0 or 1
@rxhector	-∞	That's not really intuitive, but still you can get there as shown above for +∞.
@fullcoverbetting	0
@tonimontana	½	But how can the sum of integers be no integer :P

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Winner draw:

Congratulations @rxhector you won 1 SBI!

Of course everyone also got 10 STEM for participating(check your steem engine)!
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The next contest starts in 2 days. Don't miss it!