Question 1

determine whether the recurrence relation is a linear homogeneous recurrence relation with
constant coeﬃcients.
-$$a _ { n } + a _ { n - 1 } = 1$$

Accepted Answer

The answer of determine whether the recurrence relation is a...

Question 2

Consider the recurrence relation $$a _ { n } = 2 a _ { n - 1 } + 1$$ (a) Write the associated homogeneous recurrence relation.
(b) Find the general solution to the associated homogeneous recurrence relation.
(c) Find a particular solution to the given recurrence relation.
(d) Write the general solution to the given recurrence relation.
(e) Find the particular solution to the given recurrence relation when $$a _ { 0 } = 1$$

Accepted Answer

The answer of Consider the recurrence relation \[a _ {...

Question 3

$$a _ { n } = a _ { n - 1 } + 2 n + 1 , a _ { 0 } = 5$$

Accepted Answer

The answer of \[a _ { n } = a...

Question 4

In questions ﬁnd a closed form for the generating function for the sequence.
-$$\left( \begin{array} { c } 
50 \
1
\end{array} \right) , 2 \left( \begin{array} { c } 
50 \
2
\end{array} \right) , 3 \left( \begin{array} { c } 
50 \
3
\end{array} \right) , \ldots , 50 \left( \begin{array} { c } 
50 \
50
\end{array} \right) , 0,0,0 , \ldots$$

Accepted Answer

The answer of In questions ﬁnd a closed form for...

Question 5

What form does a particular solution of the linear nonhomogeneous recurrence relation $a _ { n } = 4 a _ { n - 1 } - 4 a _ { n - 2 }$ + $F ( n )$
 have when $F ( n ) = n 2 ^ { n }$ ?

Accepted Answer

The answer of What form does a particular solution of...

Question 6

Find the solution of the recurrence relation $$a _ { n } = 3 a _ { n - 1 } \text { with } a _ { 0 } = 2$$

Accepted Answer

The answer of Find the solution of the recurrence relation...

Question 7

Find $\mid A _ { 1 } \cup A _ { 2 } \cup A _ { 3 } \cup A _ { 4 }|$ if each set  Ai has 100 elements, each intersection of two sets has 60 elements, each intersection of three sets has 20 elements, and there are 10 elements in all four sets.

Accepted Answer

Question 8

In questions solve the recurrence relation either by using the characteristic equation or by discovering
a pattern formed by the terms.
-$$a _ { n } = 5 a _ { n - 1 } - 4 a _ { n - 2 } , \quad a _ { 0 } = 1 , a _ { 1 } = 0$$

Accepted Answer

The answer of In questions solve the recurrence relation either...

Exam 8: Advanced Counting Techniques

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - $a _ { n } + a _ { n - 1 } = 1$

Correct Answer
verified

Find the solution of the recurrence relation $a _ { n } = 3 a _ { n - 1 } \text { with } a _ { 0 } = 2$

Correct Answer
verified

In questions solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = 5 a _ { n - 1 } - 4 a _ { n - 2 } , \quad a _ { 0 } = 1 , a _ { 1 } = 0$

Correct Answer
verified

Find $\mid A _ { 1 } \cup A _ { 2 } \cup A _ { 3 } \cup A _ { 4 }|$ if each set A_i has 100 elements, each intersection of two sets has 60 elements, each intersection of three sets has 20 elements, and there are 10 elements in all four sets.

Correct Answer
verified

What form does a particular solution of the linear nonhomogeneous recurrence relation $a _ { n } = 4 a _ { n - 1 } - 4 a _ { n - 2 }$ + $F ( n )$ have when $F ( n ) = n 2 ^ { n }$ ?

Correct Answer
verified

Correct Answer
verified

$a _ { n } = a _ { n - 1 } + 2 n + 1 , a _ { 0 } = 5$

Correct Answer
verified

Correct Answer
verified

Exam 8: Advanced Counting Techniques

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - an+an−1=1a _ { n } + a _ { n - 1 } = 1an​+an−1​=1

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Find the solution of the recurrence relation an=3an−1 with a0=2a _ { n } = 3 a _ { n - 1 } \text { with } a _ { 0 } = 2an​=3an−1​ with a0​=2

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In questions solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - an=5an−1−4an−2,a0=1,a1=0a _ { n } = 5 a _ { n - 1 } - 4 a _ { n - 2 } , \quad a _ { 0 } = 1 , a _ { 1 } = 0an​=5an−1​−4an−2​,a0​=1,a1​=0

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Find ∣A1∪A2∪A3∪A4∣\mid A _ { 1 } \cup A _ { 2 } \cup A _ { 3 } \cup A _ { 4 }|∣A1​∪A2​∪A3​∪A4​∣ if each set Ai has 100 elements, each intersection of two sets has 60 elements, each intersection of three sets has 20 elements, and there are 10 elements in all four sets.

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What form does a particular solution of the linear nonhomogeneous recurrence relation an=4an−1−4an−2a _ { n } = 4 a _ { n - 1 } - 4 a _ { n - 2 }an​=4an−1​−4an−2​ + F(n)F ( n )F(n) have when F(n)=n2nF ( n ) = n 2 ^ { n }F(n)=n2n ?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

an=an−1+2n+1,a0=5a _ { n } = a _ { n - 1 } + 2 n + 1 , a _ { 0 } = 5an​=an−1​+2n+1,a0​=5

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - $a _ { n } + a _ { n - 1 } = 1$

Correct Answer
verified

Find the solution of the recurrence relation $a _ { n } = 3 a _ { n - 1 } \text { with } a _ { 0 } = 2$

Correct Answer
verified

In questions solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = 5 a _ { n - 1 } - 4 a _ { n - 2 } , \quad a _ { 0 } = 1 , a _ { 1 } = 0$

Correct Answer
verified

Find $\mid A _ { 1 } \cup A _ { 2 } \cup A _ { 3 } \cup A _ { 4 }|$ if each set A_i has 100 elements, each intersection of two sets has 60 elements, each intersection of three sets has 20 elements, and there are 10 elements in all four sets.

Correct Answer
verified

What form does a particular solution of the linear nonhomogeneous recurrence relation $a _ { n } = 4 a _ { n - 1 } - 4 a _ { n - 2 }$ + $F ( n )$ have when $F ( n ) = n 2 ^ { n }$ ?

Correct Answer
verified

Correct Answer
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$a _ { n } = a _ { n - 1 } + 2 n + 1 , a _ { 0 } = 5$

Correct Answer
verified

Correct Answer
verified