What's the formula that allows a person to figure out the sum of a sequence of

numbers that are ...? Sorry I ran out of space

That are differentiated by 1.

Examples: 1+2+3+4
1+2+3+4+5+6+7
3+4+5+6

Obviously the sequences would be longer than the examples I listed.
And is there a formula that finds the products of such squences?

Like 1*2*3*4
1*2*3*4*5*6*7
3*4*5*6
 
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