Using mathematical induction, prove that this equation holds for any n 2 1: n(n + 1)(n + 2) 1x 2+ 2 x 3 +3 x 4 + .+ n(n+ 1) = 3

Q: 3n > n for every positive integer n.

A: Now, since we assumed 3k>k, we can substitute k with 3k in the inequality: 3k+1>3k Since ,…

Q: Show that P(n, 1) + P(n, 2) = (22) – 2 (2), for integers n ≥ 2.

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Q: (a) For every integer n, the number n² — n must be even. (b) For all real numbers a, a² < a¹. (c)…

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Q: the statement below true or false for n=1? ©George Mason University 2+ 4 + 6+ ... + 2n = n² + n + 1

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Q: 1+ x Σ Aa" (1 – 2)? n=0

A:

Q: (2n)! – (2n + 1)! (2n)!

A: It is required to find out , 2n! - 2n+1!2n!  For this we use factorial properties.

Q: (n-1)! Use Euler's theorem to prove that if n is an odd integer, then n divides 2 -1.

A: Using Euler theorem to prove it.

Q: How many strings of 1our decimal digits have all four digits that are different? How many strings of…

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Q: (2+i)(1+3i) – 2+ 4i= 3i O 4+2i O 3+i O 3-i0

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Q: { :Find the first 3 terms for 2n-1 (2n-1)! (−1)n+¹

A: given sequence  -1n+1x2n-12n-1!

Q: If P (n) is the statement "n + n" is even", and if P(r) is true, then prove P (r + 1) is true.

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Q: (a) Prove that (-1+iv3)" + (-1– iv3)" has either the value 2"+1 or the value –2" if n is any integer…

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Q: Which simplified choice will result in 200m20n15

A: Consider the following expression…

Q: 3) (n² + 10n+18) ÷ (n+ 5)

A: To divide the following expression.n2+10n+18÷n+5

Q: or n>3

A: Given: Mathematical statement 2Fn&gt;Fn+1 for n&gt;3. We have to check whether a given statement is…

Q: Solve for n if P(n,5)=120C(n,3)

A: The objective is to calculate the value of n, for which the following equation is…

Q: At a certain rate of compound interest, money will double in a years, money will triple in 3 years,…

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Q: In(+2)-3

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Q: Prove by using proof by contradiction: If (3n)^2 is even, then n is even.

A: Any odd integer multiply by an odd integer is odd. Any even integer multiply by an even integer is…

Q: given 7(x-1)=2(3x+2) prove x=11

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Q: (i) Deduce that the difference in the number of integers in the numerator and denominator of (* 2N N…

A: Properties of floor functions will be used.

Q: For positive integers n and k (k sn+ 1), the kth term of (a + b)n is given by

A: The binomial expansion of (a+b)^n is

Q: use gauss's trick to determine R(n)=2+3+4+...+(n-1)+n+(n+1)

A: It is known that sum of first n numbers is n(n+1)2  that is  1+2+3+----+n=n(n+1)2 Gauss trick method…

Q: ndicate the least integer n for which (3x5 + x2)4 is O(xn).

A: Solved using the binomial theorem