No, I don't want to replace infinity with -1/12. The sum 1+2+3... equaling -1/12 satisfies many mathematical rules such as linearity and stability.
To simplify, we have v=c, so M = m0 / √(1 - v^2/c^2) ~ m0c / √(c + v)√(c - v) ~ m0c / √(c + c) √(c - v) ~ m0√c / √2√(c - v) = A/√(c - v) with A = m0√c/√2.
It is therefore enough to find a divergent series M0+M1+M2+... which represents this quantity A/√(c - v) when c=v, and this series must also respect linearity, stability and other properties like that of Ramanujan, and it will be equal to M0+M1+M2+... = A/√(c - v) = m0, not -1/12.
To simplify, we have v=c, so M = m0 / √(1 - v^2/c^2) ~ m0c / √(c + v)√(c - v) ~ m0c / √(c + c) √(c - v) ~ m0√c / √2√(c - v) = A/√(c - v) with A = m0√c/√2.
It is therefore enough to find a divergent series M0+M1+M2+... which represents this quantity A/√(c - v) when c=v, and this series must also respect linearity, stability and other properties like that of Ramanujan, and it will be equal to M0+M1+M2+... = A/√(c - v) = m0, not -1/12.
