Express $ \frac{2x^2 + 7x + 9}{ (x + 1)(x + 2)(x + 3)}$ in partial fractions. Hence evaluate \( \s

Question

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)}$

Accepted Answer

$\dfrac2{x+1}-\dfrac3{x+2}+\dfrac3{x+3}$; sum $2H_{51}-3+\dfrac3{53}$, where $H_{51}=\sum_{j=1}^{51}\dfrac1j$.

Polynomials, Cubic Equations and Partial Fractions - Partial Fractions

Polynomials, Cubic Equations and Partial Fractions - Partial Fractions

Solution:

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