Problem Analysis #17

[THOUGHT] I will solve the system of equations derived from the limit condition. The limit equation gives two conditions: the coefficient of (x^{-2}) must be zero, and the constant term must be 2. This leads to the equations (a/2 + b = 0) and (a/6 - b/2 = 2). I will use sympy to solve for a and b, then compute (100(a + b)^2). [/THOUGHT] [PYTHON] from sympy import * a, b = symbols('a b') eq1 = Eq(a/2 + b, 0) eq2 = Eq(a/6 - b/2, 2) sol = solve((eq1, eq2), (a, b)) a_val = sol[a] b_val = sol[b] a_plus_b = a_val + b_val result = 100 * a_plus_b**2 print(result) [/PYTHON]

[THOUGHT] The Python code executed correctly and returned 576, which is the value of (100(a + b)^2). This result is the final answer as per the problem's requirement. [/THOUGHT] \boxed{576}