Review question

# Can we find $\sum_{r=1}^n 2/(r^2+4r+3)$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5245

## Suggestion

Express $\frac{2}{r^2+4r+3}$ in partial fractions.

Hence, or otherwise, prove that $\sum_{r=1}^n \frac{2}{r^2+4r+3}=\frac{5}{6}-\frac{2n+5}{(n+2)(n+3)}.$

We know how to rewrite the expression using partial fractions – maybe we can use this to simplify the sum?

Maybe we should try writing the sum out explicitly term by term?