The formula for the maximum number of electrons in a shell with principal quantum number 'n' is $2n^2$. K-shell (n=1): $2 \times 1^2 = 2$ electrons. L-shell (n=2): $2 \times 2^2 = 8$ electrons. M-shell (n=3): $2 \times 3^2 = 18$ electrons. N- shell (n=4): $2 \times 4^2 = 32$ electrons.