Polynomials, Cubic Equations and Partial Fractions

Suppose \( \frac{x^2 + 5x + 7}{ (x + 1)(x + 2)} = A + \frac{B}{x + 1} + \frac{C}{x + 2} \)
Find \(A, B, C\)
Hence evaluate \( \sum^{20}_{k = 1} \frac{k^2 + 5k + 7}{ (k + 1)(k + 2) }\)