Skill: series

Series Tutor Help

A one-page recap of sigma notation and the series sum formulas, plus a way to ask a tutor for a worked explanation.

1 Quick recap

The essentials on one page before you ask for help.

The three formulas

Terms in Σ_k=mⁿ: n − m + 1
Arithmetic: S_n = n/2 · (a₁ + a_n) · Geometric: S_n = a₁(1 − rⁿ)/(1 − r)

Expand a sigma by substituting the index; sum a series with the matching formula.

Stuck? Check these first

The index is not the term count: Σ_k=3¹⁰ has 10 − 3 + 1 = 8 terms.
Geometric sums use rⁿ (n, not n − 1) because the first term is a₁r⁰.
If r = 1, the formula divides by zero — the sum is just n · a₁.
Write out the first few terms when a sigma looks confusing; the pattern usually appears.

2 Ask a tutor

Tell us what you are stuck on. A tutor will follow up with a worked explanation.

Demo form: this contact form is a demonstration only. It does not send your message anywhere and no tutor will receive it — nothing leaves your browser.

3 Keep going

While you wait, review the lesson or drill practice problems.

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