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

1- Show that (n^3+3n^2+3n+1) / (n+1) is O (n2 ). Use the definition and proof of...

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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 “???” (...

Prove that 1^3 + 2^3 + · · · + n^3 = (1 + 2 +...

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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.

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