Series (FP1) Topic Review summary

Key learning points

• Build $\\sum r$, $\\sum r^2$, $\\sum r^3$ into more complex sums.
• Method of differences for rational terms that telescope.
• Induction to prove a closed form.
• Partial fractions often prepare a differences argument.
• State sums from $r=1$ to $n$ clearly with $+C$ never needed.

Worked example 1 — Sum r

$\\sum_{r=1}^{10} r$.

Working

$\\frac{10\\cdot11}{2}$.

Worked example 2 — Differences

Sum $\\sum\\left(\\frac{1}{r}-\\frac{1}{r+1}\\right)$.

Working

Classic telescope.

Worked example 3 — Practice point 1

Build $\\\\sum r$, $\\\\sum r^2$, $\\\\sum r^3$ into more complex sums.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Practice point 2

Apply this idea from the Topic Review: Method of differences for rational terms that telescope.

Working

Attempt without notes, then check the answers PDF.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.