2000002702
Level:
B
Calculate the difference: \(\left({17\above 0.0pt
16} \right) - \left({17\above 0.0pt
17} \right)\)
\( 16\)
\(17\)
\(1\)
\(0\)
Combinatorics
2000002703
Level:
B
Specify the domain of the expression: \(\left({5\above 0.0pt
n} \right) +\left({n\above 0.0pt
3} \right)\)
\( n \in \{3;4;5\} \)
\( n \in \mathbb{N},~n\leq 5\)
\( n \in \mathbb{N} \)
\( n \in \mathbb{N},~n\geq 2\)
2000002704
Level:
B
Given \(n \in \mathbb{N} \), find the sum: \(\left({n+1\above 0.0pt n} \right) + \left({n\above 0.0pt 0} \right)\)
\( n+2\)
\(n\)
\(n+1\)
\(2\)
2000002705
Level:
B
Calculate the sum: \(\left({3\above 0.0pt 0} \right) +\left({3\above 0.0pt 1} \right)+\left({3\above 0.0pt 2} \right)+\left({3\above 0.0pt 3} \right)\)
\(2^3=8\)
\(3^2=9\)
\(2\cdot 3=6\)
\( 0\)
2000002706
Level:
B
Specify the domain of the expression: \(\left({n\above 0.0pt
5} \right)+\left({n+1\above 0.0pt
1} \right)\)
\( n \in \mathbb{N},~n\geq 5\)
\( n \in \mathbb{N},~n\leq 5\)
\( n \in \mathbb{N},~n\geq 6\)
\( n \in \mathbb{N},~n\geq 4\)
2000002801
Level:
B
Simplify for \( n \in \mathbb{N}\) and \(n\geq 3\):
\[\frac{(n-3)!}{(n-2)!}\]
\(\frac{1}{n-2}\)
\( n-3\)
\(n-2\)
\(\frac{1}{n-3}\)
2000002802
Level:
B
Simplify for \( n \in \mathbb{N}\):
\[\frac{n!\cdot n!}{(n-1)!\cdot (n+1)!}\]
\( \frac{n}{n+1}\)
\( n^2 \)
\( \frac{n}{n-1}\)
\( \frac{1}{n-1}\)
2000002803
Level:
B
Simplify for \( n \in \mathbb{N}\):
\[\frac{2\cdot n!}{(n-1)!}\]
\( 2n\)
\( 2\cdot n!\)
\(\frac{2}{n-1}\)
\(\frac{2}{(n-1)!}\)
2000002804
Level:
B
Specify the domain of the expression:
\[\frac{2\cdot (n-4)!}{(n-1)!}\]
\( n \in \mathbb{N},~n \geq 4 \)
\( n \in \mathbb{N},~n \geq 5 \)
\( n \in \mathbb{N} \)
\( n \in \mathbb{N},~n \geq 2 \)
2000002805
Level:
B
Specify the domain of the expression:
\[\frac{(n+4)!}{(n+5)!}\]
\( n \in \mathbb{Z},~n\geq -4\)
\( n \in \mathbb{Z},~n\geq -5\)
\( n \in \mathbb{N}\)
\( n \in \mathbb{Z},~n\leq -5\)