Series summary

Key learning points

• Use linearity of summation with known formulae.
• Prove proposed sum formulae by induction.
• Partial fractions can create telescoping terms.
• State the values of $n$ for which a result holds.

Worked example 1 — Linearity

How do you sum $\sum(3k+1)$?

Working

Pull out constants; use $\sum k=\frac{n(n+1)}{2}$.

Worked example 2 — Use linearity of summation with known formulae

Use this method from the Series sheet: Use linearity of summation with known formulae.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 3 — Prove proposed sum formulae by induction

Use this method from the Series sheet: Prove proposed sum formulae by induction.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 4 — Partial fractions can create telescoping terms

Use this method from the Series sheet: Partial fractions can create telescoping terms.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 5 — State the values of for which a result holds

Use this method from the Series sheet: State the values of $n$ for which a result holds.

Working

Each key learning point matches a question type on the printable worksheet.

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.