Question 92349
x^2 + x - k
That means you want factors of -k that sum to 1....
Plug:
~~~ No Negative Values Work
k = -2 ... nope
k = -1 ... nope
k = 0 ... yes
k = 1 ... nope
k = 2 ... yes
k = 3 ... nope
k = 4 ... nope
k = 5 ... nope
k = 6 ... yes
k = 7 ... nope
k = 8 ... nope
k = 9 ... nope
k = 10 ... nope
k = 11 ... nope
k = 12 ... yes
~~~Skip a Few
k = 20 ... yes
Works: 2,6,12,20 ....
+2,+4,+6,+8,+10 ....
Arithmetic Sum:
S(k) = (k/2)(k1 + kx) ... where k1 is the first term and kx is the last term
S(k) = (k/2)(2 + k)
S(k) = k + k^2
First term: S(1) = 1 + 1^2 = 2
Second term: S(2) = 2 + 2^2 = 6
Kth term: S(k) = k + k^2 including zero