Různé řady

Úloha číslo: 2911

Vyšetřete konvergenci řad

  • Varianta 1

    \(\displaystyle \sum_{n=1}^{\infty}\frac{n+1}{n(n+2)} \).

  • Varianta 2

    \(\displaystyle \sum_{n=1}^{\infty}\sqrt\frac{n-1}{2n}\).

  • Varianta 3

    \(\displaystyle \sum_{n=1}^{\infty}\frac{n+1}{(n+1)\sqrt{n+1}-1} \)

  • Varianta 4

    \(\displaystyle \sum_{n=1}^{\infty}\left(\frac{1+n^2}{1+n^3}\right)^2 \).

  • Varianta 5

    \(\displaystyle \sum_{n=1}^{\infty}\frac1{(n+3)\sqrt{n}} \).

  • Varianta 6

    \(\displaystyle \sum_{n=1}^{\infty}\frac{\sqrt n}{n^3+1} \).

  • Varianta 7

    \(\displaystyle \sum_{n=1}^{\infty}\sqrt[n]{\frac1{1000}} \).

  • Varianta 8

    \(\displaystyle \sum_{n=1}^{\infty}\frac{2n-1}{\sqrt{2^n}} \)

  • Varianta 9

    \(\displaystyle \sum_{n=1}^{\infty}\frac1{n\cdot3^n} \).

  • Varianta 10

    \(\displaystyle \sum_{n=1}^{\infty}\frac{n^5}{2^n+3^n} \).

  • Varianta 11

    \(\displaystyle \sum_{n=1}^{\infty}\frac{1!+2!+3!+…+n!}{(2n)!} \).

  • Varianta 12

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

  • Varianta 13

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

  • Varianta 14

    \(\displaystyle \sum_{n=1}^{\infty}\frac{2+\cos n}{n+\ln n} \)

  • Varianta 15

    \(\displaystyle \sum_{n=1}^{\infty}\frac{\sin n}{n(n+2)} \)

  • Varianta 16

    \(\displaystyle \sum_{n=1}^{\infty}\sin\frac1n \).

  • Varianta 17

    \(\displaystyle \sum_{n=1}^{\infty}\sin\frac1{n^2} \).

  • Varianta 18

    \(\displaystyle \sum_{n=1}^{\infty}e^{\sqrt[-3]n} \).

  • Varianta 19

    \(\displaystyle \sum_{n=1}^{\infty}\frac{\ln n}{n} \)

  • Varianta 20

    \(\displaystyle \sum_{n=2}^{\infty}\frac{\sqrt{n^2+1}-n}{\log^2 n}\ . \)

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