B

1003107301

Level: 
B
We are given the sequence \( \left( \frac{n+1}n \right)^{\infty}_{n=1} \). Find the recursive formula of such sequence.
\( a_1=2\,;\ a_{n+1}=a_n\frac{n(n+2)}{(n+1)^2},\ n\in\mathbb{N} \)
\( a_1=2\,;\ a_{n+1}=a_n\frac{n(n+2)}{(n+1)},\ n\in\mathbb{N} \)
\( a_1=1\,;\ a_{n+1}=a_n\frac{n(n+2)}{(n+1)^2},\ n\in\mathbb{N} \)
\( a_1=2\,;\ a_{n+1}=a_n\frac{n(n-2)}{(n+1)^2},\ n\in\mathbb{N} \)

1103109303

Level: 
B
Consider an equation \( x^n+b=0 \), where \( n \) is a positive integer and \( b \) is a real number. The points that correspond to the roots of the equation are marked in the figure as black points. Find the equation.
\( x^8 - 256 = 0 \)
\( x^8 + 256 = 0 \)
\( x^4 + 16 = 0 \)
\( x^4 - 16 = 0 \)
\( x^6 - 64 = 0 \)
\( x^6 + 64 = 0 \)

1003076513

Level: 
B
If two of the values of \( \sin\alpha \), \( \cos\alpha \), \( \mathrm{tg}\alpha\) and \( \mathrm{cotg}\alpha \) are negative, then \( \alpha \) belongs to the interval
\( \left(\pi; \frac{3\pi}2 \right) \).
\( \left(0; \frac{\pi}2 \right) \).
\( \left(\frac{\pi}2; \pi\right) \).
\( \left( \frac{3\pi}2; 2\pi \right) \).