- #1

FeDeX_LaTeX

Gold Member

- 437

- 13

I don't know how to prove this conjecture I've made;

For the polynomial equation

[tex]-\sum_{n=0}^{\infty}k^{n}=0[/tex]

there exist no real solutions greater than 2, no matter how large the value of n.

How do I show that this is true?

If it's a little unclear, what I mean is, for example, if you had the equation

k^30 - k^29 - k^28 ... - k - 1 = 0, k doesn't exceed 2.

So even if you start from 1000, or 100000000000, or

*any*number, you will never find a solution greater than 2.

Thanks.