Lots of Questions . . .

[BlueHorseshoe 10]

Hello,

 

A series of dull questions relating to something that I'm trying to do . . .

 

1)

 

N! or 'N Factorial' is the product of all whole integers with a value less than or equal to N.

 

So for example:

 

5! = 1 x 2 x 3 x 4 x 5 = 120

 

But if these numbers were summed rather than multiplied for all whole integers less than N, does this have a specific term?

 

2)

 

Next, is there a way in EasyLanguage to 'step' summation?

 

This used to be possible in BASIC with the STEP command. So a summation of whole integers less than 100 with a step size of 5 would be 5 + 10 + 15 . . . + 100.

 

3)

 

And finally . . .

 

Suppose you have people moving into a town over ten days. On the first day 10 people will move, and on the tenth day 100 people will move. If you know that the increase will be linear then you can work out how many people will have moved in by the tenth day (the thing I don't know the name of that's a bit like the factorial but with summation) . . . 550.

 

If this increase wasn't linear but followed some other function instead, how would I go about calculating the number of people in the town after 10 days? Any generalisable example will do.

 

Many thanks to anyone who can help,

 

BlueHorseshoe

[BlueHorseshoe 10]

Also, can anybody explain to me in simplistic terms (I'm not a mathematician) whether this would be a form of exponentiation?

 

n = ( n[1] * k ) + ( y * ( 1 - k ) ) ;

 

What is the differnce between "power laws" and exponentiation, exactly?

 

Cheers,

 

BlueHorseshoe

[BlueHorseshoe 10]

But if these numbers were summed rather than multiplied for all whole integers less than N, does this have a specific term?

 

I have found the answer to my first question above.

 

Apparently the additive analog of the factorials is the triangular number.

 

BlueHorseshoe