Monotonic sequences

Task number: 2862

Decide whether the following sequences are monotonic and, if so, determine whether they are increasing, decreasing, non-decreasing or non-increasing.

  • Variant 1

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

  • Variant 2

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

  • Variant 3

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

  • Variant 4

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

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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