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This is the first Topic I've posted at (the very cool) Physics Forums site so go easy on me. My English is very far from perfect so some used terms may not be used correctly... :)

Anyways... I was writing a script for a website and a mathematics question popped up.

The numbers 1, 3, 6, 10, 15, 21... can be received by summing group of numbers where the first is 0 and each subsequent number is greater then the previous with 1.

for example:

1 = 0 + 1

3 = 0 + 1 + 2

6 = 0 + 1 + 2 + 3

10 = 0 + 1 + 2 + 3 + 4

and so on...

My 2 questions:

(0) I'd love to know if it possible to determine if a given number is among the list of numbers that can be received from such summing.

(1) And if the above is too complicated to discuss here - can you tell me the term in mathematics that describes such summing (if such exists) so I can google the topic?

Any help would be fantastic.

Cheers.

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# Summing Gradually Changing Numbers

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