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Problem: Examine the convergence of the series: \[ \sum_{n=0}^{\infty} \frac{2 n+n^{5}}{3 n^{7}-7} . \]

2.10.41 Number series

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Problem: Examine the convergence of the series: \[ \sum_{n=0}^{\infty} \frac{n !}{n^{2}+1} . \]

2.10.42 Number series

0.51 $

Problem: Examine the convergence of the series: \[ \sum_{n=0}^{\infty}\left(\frac{3}{4 n+7}\right)^{n} \text {. } \]

2.10.43 Number series

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Problem: Determine the type of convergence of the series: \[ \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{(n+2)^{n}} \text {. } \]

2.10.44 Number series

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Problem: Determine the type of convergence of the series: \[ \sum_{n=1}^{\infty} \frac{(-1)^{n} 6 n}{2 n} \text {. } \]

2.10.45 Number series

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Problem: Determine the type of convergence of the series: \[ \sum_{n=1}^{\infty}(-1)^{n+1}\left(\frac{3 n^{2}+5}{2 n^{2}-n}\right)^{n} . \]

2.10.46 Number series

0.51 $

Problem: Determine the type of convergence of the series: \[ \sum_{n=1}^{\infty} \frac{(-1)^{n}(4 n-1)}{n !} \]

2.10.47 Number series

0.51 $

Problem: A binary relation is given: \( R=\{(x, y) \mid x, y \in \mathbb{N} \wedge \) \( y: x\} \). Find: \( \delta_{R}, \rho_{R}, R^{1}, R \circ R^{-1}, R \circ R \).

6.2.7 Binary relations

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Problem: A binary relation is given: \( R=\{(x, y) \mid x, y \in \mathbb{N} \wedge \) \( x: y\} \). Find: \( \delta_{R}, \rho_{R}, R^{1}, R \circ R^{-1}, R \circ R \).

6.2.8 Binary relations

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Problem: A binary relation is given: \( R=\{(x, y) \mid x, y \in D \wedge \) \( y+x \leq 0\} \). Find: \( \delta_{R}, \rho_{R}, R^{1}, R \circ R^{-1}, R \circ R \).

6.2.9 Binary relations

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Problem: A binary relation is given: \( R=\{(x, y) \mid x, y \in D \wedge \) \( 2 x \geq 3 y\} \). Find: \( \delta_{R}, \rho_{R}, R^{1}, R \circ R^{-1}, R \circ R \).

6.2.10 Binary relations

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Problem: A binary relation is given: \( R=\{(x, y) \mid x, y \in \) \( \left.\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \wedge y \geq \sin x\right\} \). Find: \( \delta_{R}, \rho_{R}, R^{1}, R \circ R^{-1}, R \circ R \).

6.2.11 Binary relations

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3) Problem: Calculate the volume of the solid \( V \), bounded by the given surfaces: \[ V: z=30\left((x+1)^{2}+y^{2}\right)+1, \quad z=60 x+61 . \]

9.5.5 Volume of a solid

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3) Problem: Calculate the volume of the solid \( V \), bounded by the given surfaces: \[ V:\left\{\begin{array}{l} x^{2}+y^{2}=4 \\ z=\sqrt{8-x^{2}-y^{2}} \\ z=0 \end{array}\right. \]

9.5.11 Volume of a solid

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(3) Problem: Calculate the volume of the solid \( V \), bounded by the given surfaces: \[ V:\left\{\begin{array}{l} y=\sqrt{x^{2}+z^{2}} \\ y=2-x^{2}-z^{2} \end{array}\right. \]

9.5.12 Volume of a solid

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