okay.....if you accept that the sequence 1+2+3+4.....=-1/12, I think I have determined a finite value of infinity. To find the value of the sums of all natural numbers up to a number, you can use the equation ((x^2)+x)/2. An example would be 4. 4+3+2+1=10. ((4^2)+4)/2 also equals 10. following this logic, ((x^2)+x)/2=-1/12 is true for the above sequence. this can be rearranged to (x^2)+x+1/6 This is the resulting quadratic equation. Using the quadratic formula, one obtains the x intercepts as (-3+-(sqrt3))/6. and since x is infinity in this situation (since the highest value is infinity), the x intercepts are the values of infinity in the equation. Therefore, by assigning a value of -1/12 to riemann zeta(-1), you also assign finite values to infinity, approximately -0.211324.... and -0.788675.... If there is any faulty reasoning, please remember I'm 15 and I most likely have no clue what I'm talking about.