<p>Express \( \frac{2x^2 + 7x + 9}{ (x + 1)(x + 2)(x + 3)}\) in partial fractions.<br>Hence evaluate \( \sum^{50}_{k = 1} \frac{2k^2 + 7k + 9}{ (k + 1)(k + 2)(k + 3)}\)<br>(Designed so the decomposition telescopes unexpectedly.)</p>

Express \( \frac{2x^2 + 7x + 9}{ (x + 1)(x + 2)(x + 3)}\) in partial fractions.
Hence evaluate \( \sum^{50}_{k = 1} \frac{2k^2 + 7k + 9}{ (k + 1)(k + 2)(k + 3)}\)
(Designed so the decomposition telescopes unexpectedly.)

Polynomials, Cubic Equations and Partial Fractions

Polynomials, Cubic Equations and Partial Fractions