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Calculus · Series-And-Sums

Convergence of 1/n

\frac{1}{n}

Step by step

  1. \sum_{n=1}^{\infty} \frac{1}{n}

    Does this series converge?

  2. \lim_{n\to\infty} \frac{1}{n} = 0

    Divergence test: if the terms do not go to 0 the series cannot converge.

  3. \lim \left|\frac{a_{k+1}}{a_k}\right| = \lim \left|{\frac{n}{n + 1}}\right| = 1

    Ratio test: < 1 converges, > 1 diverges, = 1 says nothing.

  4. \text{diverges}

    The series diverges.

Reveal the answer
\text{diverges}