[1/1] Padé of exp: (1+x/2)/(1-x/2); leading O(x³) residual 1/12

Sympy-exact Taylor-to-order-3 comparison of the [1/1] Padé approximant of e^x against its Taylor series. Step 1 — the Padé rational: P(x) = (1 + x/2)/(1 − x/2); its order-3 Taylor expansion is 1 + x + x²/2 + x³/4. Step 2 — Taylor of e^x…