1. prove s(n, k) = s(n − 1, k − 1) − (n − 1)s(n −...

1. prove

s(n, k) = s(n − 1, k − 1) − (n − 1)s(n − 1, k).

2. What is ∑n k=0 s(n, k)?

Expert Solution

Colby Messinger answered 2 years ago

Prove combinatorially: {{n \ choose x)= {{k+1 \ choose n-1) This question is asking to prove...

Prove combinatorially: {{n \ choose x)= {{k+1 \ choose n-1) This question is asking to prove combinatorially whether n multi-choose k is equal to k+1 multi-choose n-1 Thank you

1.Prove that{2k+1:k∈N}∩{2k2 :k∈N}=∅. 2.Give two examples of ordered sets where the meaning of ” ≤ ”...

1.Prove that{2k+1:k∈N}∩{2k2 :k∈N}=∅. 2.Give two examples of ordered sets where the meaning of ” ≤ ” is not the same as the one used with the set of real numbers R.

Let S_k(n) = 1^k + 2^k + ··· + n^k for n, k ≥ 1. Then,...

Let S_k(n) = 1^k + 2^k + ··· + n^k for n, k ≥ 1. Then, S_4(n) is given by S_4(n)= n(n+1)(2n+1)(3n^2 +3n−1)/ 30 Prove by mathematical induction.

Using S ≈ N k, estimate the entropy of the sun.

Given an array A[1..n], with distinct values and k with 1 ≤ k ≤ n. We...

Given an array A[1..n], with distinct values and k with 1 ≤ k ≤ n. We want to return the k smallest element of A[1.....n], in non-decreasing order. For example: A = [5, 4, 6, 2, 10] and k = 4, the algorithm returns [2, 4, 5, 6]. There are at least the following four approaches: a. heapify A and then extract k elements one by one b. sort the array (e.g. using MergeSort or HeapSort) and then read the...

Prove that 3 divides n^3 −n for all n ≥ 1.

Let S={1,2,3,6} and define the relation ~ on S2 by (m,n) ~ (k,l) for m+l=n+k Show...

Let S={1,2,3,6} and define the relation ~ on S2 by (m,n) ~ (k,l) for m+l=n+k Show that it is an equivalent relation Find the number of different equivalent classes and write all of them

1. Using the solow growth model, given y(K) = k^0.4, S=0.20, depreciation rate=0.04 and n=1%, a....

1. Using the solow growth model, given y(K) = k^0.4, S=0.20, depreciation rate=0.04 and n=1%, a. What is the steady-state level of capital per worker? b. What is the steady-state of output per worker? c. What is the steady-state level of consumption per worker? 2. Now assume population growth is instead-0.5% (approximately the growth rate when every couple has 1.7 children), but that all other parameters stay the same. a. What is the new steady-state output per worker? Is it...

Prove this is true: The sequence {4k + 3} where k ∈ N contains infinitely many...

Prove this is true: The sequence {4k + 3} where k ∈ N contains infinitely many primes, but the sequence {4k + 2} does not.

Prove this is true: The sequence {4k + 3} where k ∈ N contains infinitely many...

Prove this is true: The sequence {4k + 3} where k ∈ N contains infinitely many primes, but the sequence {4k + 2} does not. Show your work.

Question

1. prove s(n, k) = s(n − 1, k − 1) − (n − 1)s(n −...

Solutions

Expert Solution

Related Solutions

Prove combinatorially: {{n \ choose x)= {{k+1 \ choose n-1) This question is asking to prove...

1.Prove that{2k+1:k∈N}∩{2k2 :k∈N}=∅. 2.Give two examples of ordered sets where the meaning of ” ≤ ”...

Let S_k(n) = 1^k + 2^k + ··· + n^k for n, k ≥ 1. Then,...

Using S ≈ N k, estimate the entropy of the sun.

Given an array A[1..n], with distinct values and k with 1 ≤ k ≤ n. We...

Prove that 3 divides n^3 −n for all n ≥ 1.

Let S={1,2,3,6} and define the relation ~ on S2 by (m,n) ~ (k,l) for m+l=n+k Show...

1. Using the solow growth model, given y(K) = k^0.4, S=0.20, depreciation rate=0.04 and n=1%, a....

Prove this is true: The sequence {4k + 3} where k ∈ N contains infinitely many...

Prove this is true: The sequence {4k + 3} where k ∈ N contains infinitely many...