Limits by definition

Task number: 2863

Determine the limits of the following sequences by definition:

  • Variant 1

    \(\displaystyle \left\{ \frac1{n} \right\}_{n=1}^\infty\)

  • Variant 2

    \(\displaystyle \left\{ \frac1{\sqrt{n}} \right\}_{n=1}^\infty\)

  • Variant 3

    \(\displaystyle \left\{ \log n \right\}_{n=1}^\infty\)

  • Variant 4

    \(\displaystyle \left\{ \frac1{1+n^2} \right\}_{n=1}^\infty\)

  • Variant 5

    \(\displaystyle \left\{ \frac{n+1}{n+2} \right\}_{n=1}^\infty\)

  • Variant 6

    \(\displaystyle \left\{ \sqrt[n]{a}\right\}_{n=1}^\infty\), where \(a\) is a positive real number.

  • Variant 7

    \(\displaystyle \left\{ \sin \frac1n\right\}_{n=1}^\infty\).

Difficulty level: Moderate task
Proving or derivation task
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