I think you forgot to close your brackets.
Simplifying from the innermost brackets:
\(y + 2\left(y + 3\left(y + 4 \left(y + \dfrac1{24}\right)\right)\right) = 100\\ y + 2 \left(y + 3 \left(5y + \dfrac16\right)\right) = 100\\ y + 2 \left(16y + \dfrac12\right) = 100\\ 33y +1 = 100\\ y = 3\)