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Graduate · Real Analysis

Series, rigorously

54 problems in this skill, each with a solver-verified answer key. Answers are checked the moment you submit — with a hint if you want one and a worked solution afterwards.

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

  1. Warm-up

    Compute the exact sum of the convergent geometric series ∑n=0∞26n\displaystyle \sum_{n=0}^{\infty} \dfrac{2}{6^{n}}.

  2. Warm-up

    Compute the exact sum of the convergent geometric series ∑n=0∞53n\displaystyle \sum_{n=0}^{\infty} \dfrac{5}{3^{n}}.

  3. Warm-up

    Compute the exact sum of the convergent geometric series ∑n=0∞36n\displaystyle \sum_{n=0}^{\infty} \dfrac{3}{6^{n}}.

Problems shown under their original terms: Generated (template, solver-computed).

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