Write a combinatorial proof for 1 n + 2 ( n − 1 ) + 3...

Write a combinatorial proof for 1 n + 2 ( n − 1 ) + 3 ( n − 2 ) + ⋯ + ( n − 1 ) 2 + n 1 = ( n + 2 choose 3 ) .

Expert Solution

orchestra answered 1 year ago

Show that (a)Sn=<(1 2),(1 3),……(1 n)>. (b)Sn=<(1 2),(2 3),……(n-1 n)> (c)Sn=<(1 2),(1 2 …… n-1 n)>

proof a circle is divided into n congruent arcs (n ?? 3), the tangents drawn at...

proof a circle is divided into n congruent arcs (n ?? 3), the tangents drawn at the endpoints of these arcs form a regular polygon.

Data Structure: 1. Write a program for f(n) = 1^2+2^3+…+n^2. (i^2 = i*i) 2. If you...

Data Structure: 1. Write a program for f(n) = 1^2+2^3+…+n^2. (i^2 = i*i) 2. If you have the following polynomial function f(n)=a0 +a1 x + a2x2+…+an xn , then you are asked to write a program for that, how do you do? 3. Write a function in C++ to sort array A[]. (You can assume that you have 10 elements in the array.) 4. Analyze the following program, tell us what does it do for each location of “???” (...

Which codes add 1 to integer n? 1) n=n+1; 2) n++; 3)++n; 4) n+=1; 5) n=--n+2

(a) Find the limit of {(1/(n^(3/2)))-(3/n)+2} and use an epsilon, N argument to show that this...

(a) Find the limit of {(1/(n^(3/2)))-(3/n)+2} and use an epsilon, N argument to show that this is indeed the correct limit. (b) Use an epsilon, N argument to show that {1/(n^(1/2))} converges to 0. (c) Let k be a positive integer. Use an epsilon, N argument to show that {a/(n^(1/k))} converges to 0. (d) Show that if {Xn} converges to x, then the sequence {Xn^3} converges to x^3. This has to be an epsilon, N argument [Hint: Use the difference...

Use a direct proof to prove that 6 divides (n^3)-n whenever n is a non-negative integer.

Use Java for the following; Part 1 n!= n * (n –1)* (n–2)* ...* 3 *...

Use Java for the following; Part 1 n!= n * (n –1)* (n–2)* ...* 3 * 2 * 1 For example, 5! = 5 * 4 * 3 * 2 * 1 = 120 Write a function called factorial that takes as input an integer. Your function should verify that the input is positive (i.e. it is greater than 0). Then, it should compute the value of the factorial using a for loop and return the value. In main, display...

Define the following function f(n) = 5(2^n)-(2^(n-1)), n ≥ 1. Write a recursive definition for the...

Define the following function f(n) = 5(2^n)-(2^(n-1)), n ≥ 1. Write a recursive definition for the function f(n)? Consider the following recurrence: an= 2an-1 + 3 (where a1 = 1). Compute the values of an for n ≤ 5. Find a solution for the recurrence definition and validate its correctness. Consider the following recurrence: an=2an-1 +an-1an-2 (where a1 = 1). Compute the values of an for n ≤ 5.

proof: L t^(n+1)f(t)=(-1)^(n+1)(d^(n+1)/ds^(n+1))*F(s)

proof: L t^(n+1)*f(t)=(-1)^(n+1)*(d^(n+1)/ds^(n+1))*F(s)

convergent or divergent infinity sigma n = 1 sqrt(n^5+ n^3 -7) / (n^3-n^2+n)

Question