Express \[\frac{2}{r^2+4r+3}\] in partial fractions.
Hence, or otherwise, prove that \[\sum_{r=1}^n \frac{2}{r^2+4r+3}=\frac{5}{6}-\frac{2n+5}{(n+2)(n+3)}.\]
Counting & Binomials
Question
Express \[\frac{2}{r^2+4r+3}\] in partial fractions.
Hence, or otherwise, prove that \[\sum_{r=1}^n \frac{2}{r^2+4r+3}=\frac{5}{6}-\frac{2n+5}{(n+2)(n+3)}.\]