n E(-1)* k + k)"-1, n2 1. k=0

Q: What is the sum of <4 + <3

A: The sum of &lt;4+&lt;3 is:

Q: Show for all natural numbers n >= 3 that [(1 + (1/n))^n] < n.

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Q: Prove or Disprove: |Q| = |Q^200|, where Q is the set of rational numbers.

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Q: Find all integers n such that (n^2) - 1 is prime.

A: n² - 1 = (n-1)(n+1)  Now, if (n² - 1) needs to be a prime, then, either n-1 is equal to 1 or, n+1 is…

Q: prove that 3^n is greater than n^3 for all n greater than or equal to 4

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Q: Prove that for all divides natural numbers nt 7^-2^.

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Q: For all integers n, if 6 | n, then 9 | ((n^2) + 21n/2)

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Q: Show that this number is Irrational number

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Q: d) limnoo 1 •k=1 an e) limn 1 48x = =공 6 4

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Q: what are the integers for 6<x<7 with a line under each less than sign

A: To determine: The integers for 6 &lt; x &lt; 7 with a line under each less than sign. It means, 6 ≤…

Q: Prove that 4 does not divide n^2 + 2 ( n squared plus 2)

A: We will show that 4 does not divide n2+2 by method of contradiction i.e , we will assume to the…

Q: of all positive integers Find the sum less than 200

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Q: Provide either a proof or a counterexample for  For all positive real numbers x, x^2 - x ≥ 0

A: According to the given information, it is required to prove the given equality or give a counter…

Q: Suppose An = 2n^2 + 6n + 6. Find the closed formula for the sequence of differences by computing An…

A: As per our question, we need to find the closed form of an-an-1×an-an-1 First find an-1 and then…

Q: Suppose I choose two numbers from the set {1, 2, 3,… 100}. How many have an even sum? Show all work.

A: Introduction: There are total 100 numbers between 1 and 100. Out of these, 50 numbers are odd: 1, 3,…

Q: Show that set & contains no greatest rational number 2 = { reQirs 0³ U{ re Qir²<2}

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Q: (4) For all natural numbers n, 4^n - 1 is a multiple of 3

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