Review question

Can we sum $r(r+1)(r+3)$ for $r$ from $1$ to $n$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5246

Suggestion

Evaluate:

1. $\sum_{r=1}^n \dfrac{1}{r(r+1)(r+3)}$.

How can we rewrite $\dfrac{1}{r(r+1)(r+3)}$ in a way that might be useful? Could we use partial fractions?

Or alternatively, if we write the numerator as $r+1-r$, can we now split the fraction into two fractions which both have terms that cancel?