Can anyone guess what this algebraic expression is for?

Question

(b^2)/(2i) + b/2 - (a^2)/(2i) + a/2

Note: "i" is being used as a variable, not an imaginary number.

Hint: It has something to do with adding.

Further hints:

I guess it could help to look at the factored form of this problem.

"b" should be larger than "a" when storing your variables.

"i" stands for "increment".

It is somewhat similar to the factoral operation.

Answer 1

It is the sum of the numbers from a to b in steps of i.

For instance, a = 5, b = 13 and i = 2 give

(13^2)/4 + 13/2 - 5^2/4 + 5/2 = 45
5 + 7 + 9 + 11 + 13 = 45



Derivation: the sum

[1] ... a + (a+i) + (a+2i) + ... + (b-2i) + (b-i) + b

has 1+(b - a)/i = (b - a + i)/i terms. Grouping the first and last, second and second last, etc. we find that it is equal to

[2] ... (a + b) + (a + b) + ... + (a + b)

with (b - a + i)/2i terms, i.e. it is equal to

[3] ... (a + b) * (b - a + i)/2i

Expanding this we get your formula.

Answer 2

That simplifies into (b+a)/2 + (b^2-a^2)/2i.

Multiply both of them by 2i and you get this:

(bi + ai) + (b^2 - a^2)

Take an i out of the first one and take the square root out of the second and you get this:

i(b + a) + (b + a)(b - a)

That's the farthest I could get.

Answer 3

1/2i {b^2 - a^2} +b/2 + a/2 =
1/i (b-a)(b/2+a/2) + (b/2 + a/2) =
{ 1/i(b-a) + 1 } (b/2+a/2) =gmpfffffffff

Answer 4

Polynomial? But, we don't play those games, here... too few rocket scientists! And, they are here to relax, not work!