Mathematics Homework Solutions
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- What is the value of 1+2+3....+(p-1) (mod p)? - What is the value of 1 + 2 + 3.....+(p-1) (mod p)?
- Discrete Math problems: Mathematical induction - 1.Use mathematical induction to prove that 2-2*7+2*7^2-.....+2(-7)^n=(1-(-7)^n+1)/4 whenever n is a nonnegative integer. 2.Show that 1^3+2^2+....n^3=[n(n+1)/2]^2 whenever n is a positive integer. ...
- dense subsets of the unit circle in the complex plane - to find theta, and prove that {e^{in theta} : n nonnegative integer} is a dense subset of the unit circle.
- Using Permutations and Combinations - How many distinct nonnegative integer solutions are there to the equation x1 + x2 + x3 =7 in which x1 is greater than or equal to 3.
- Discrete Math : Number of Solutions to Equations - a) Let n and r be positive integers. Explain why the number of solutions of the equation x1 + x2 + … + xn = r, where xi is a nonnegative integer for i = 1, 2, 3, …, n, equals the number of r-combinat ...
