Can you draw any conclusions?
We found out that all the odd numbers can be made by two consecutive
numbers. We also found out that numbers to the power of 2 (2, 4, 8, 16) can
never be made by adding together consecutive numbers together.
Can you support your conclusions with convincing arguments or
proofs?
To prove this conclusion we used all the numbers up to 30 and found all
the possible consecutive sums that added to them here are a few
examples:
9: 4+5, 2+3+4
15: 7+8, 1+2+3+4+5, 4+5+6
16:
23: 11+12
30: 9+10+11, 4+5+6+7+8, 6+7+8+9
What are the possible next questions?
To explore this investigation further, we
could maybe use decimal points or minus
numbers. Also, we could try using
subtraction, multipling or dividing, instead
of just adding. To continue with the same
kind of question, we could keep going all
the way to 100 or even 1000!