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Any help with these would be great :) 1. Use mathematical induction to prove the statement 4 + 8 + 12+…+4n = 2n(n+1) is true for all positive integers n. 2. When using math induction to prove that (n4 - 4n2) is divisible by 3 for all natural numbers. First, we will assume that (k4 - 4k2) is...

Hey everyone, I'm having quite a bit of trouble finding the nth term of these problems, any help (and answers) would be greatly appreciated, Thanks :) 1. Find the nth term of the arithmetic sequence where a1 = 5000 and d = -100. 2. Find the nth term of the geometric sequence where a(1) = 4...

Hey everyone, I'm having quite a bit of trouble finding the nth term of these problems, any help (and answers) would be greatly appreciated, Thanks :) 1. Find the nth term of the arithmetic sequence where a1 = 5000 and d = -100. 2. Find the nth term of the geometric sequence where a(1) = 4...

1. Find the missing sides and angle for the following triangle: B = 43.4 degrees, b = 3.68, a = 20.5 - a : A = 20.7 degrees, C = 114.9 degrees, c = 26.18 - b : A = 21.7 degrees, C = 114.9 degrees, c = 24.18 - c : A = 22.7 degrees, C = 114.9 degrees, c = 28.18 - d : No such triangle exists...

1. Find angle theta that lies between u= <1, -2, 2> and v = <2, 2, 2> -a: 78.9 degrees -b: 15.8 degrees -c: 80.4 degrees -d: 90 degrees 2. Given u = -i + 2j + 2k and v = 4i + k, find u x v - a: – 4i – 0j + 2k - b: 2i + 9j - 8k - c: 6i – j + 4k - d: – 2i – 9j + 8k

1. Factor the following polynomial completely: x^4+4x^3+12x^2+36x+27 a. (x - 1)(x - 3)(x - 3i)(x + 3i) b. (x + 1)(x + 3)(x - 3i)(x + 3i) c. (x - 6)(x + 6)(x - 3i)(x + 3i) d. (x - 1)(x + 3)(x - 3)(x + 3) 2. Divide using Long Division: (11x^2 + 79x - 72) / (x + 8) a. (11x + 9) b. (11x...

1. Using the leading coefficient test, determine the eventual rise and fall of f(x) = -2x5+ x3- 7. 2. List all of the asymptotes for the function: f(x) = x^2 - 4 / x^2 - 9 3. List the possible rational roots for the function whose equation is f(x) = 2x^3 + bx^2 - cx + 10 , where b and c are...