0 Explain why it is true that for any positive integer n, D" 0

Q: O Prove 1+3+ 9+27+ ·+ 3n-1 = 3"-1 for any positive integer n. %3D

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Q: need bits after (d)

A: Note- Since you have posted multiple questions we will solve only 3 sub parts as per guideline…

Q: Find a formula for 1/2+1/4+1/8+.+ 1/2h by examining the values of this expression for small values…

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Q: Write TRUE if the statement is true, otherwise, write FALSE. 3. For all prime numbers n, 2^n − 1…

A: To prove:For all prime numbers n, 2n− 1 is prime. Suppose on the contrary that 2n-1 is not prime.…

Q: N is a natural number. How many values of 'n' can take if ( n! ) Is a multiple of 2 power 25 but not…

A: The highest power of 2 that will multiple of n! is n2+n22+n23+n24+n25+... and so on If we take n=20,…

Q: (6.1) Prove if r is a positive, even integer then 10* – 1 is divisible by 11. (6.2) Prove if r is a…

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Q: Show that 3+ V5 is irational number

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Q: 5. (CLO3) Prove that (n+3) = ("+²) + (+¹) + () for every positive integer n.

A: We need to prove        n+3C2 = n+2C2 + n+1C1 + nC0    We know, for any positive integer n and k…

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Q: Prove that the statement is true for every positive integer n.

A: We know that the sum of a geometric series of the form: a+ar+ar2+ar3+...........+arn-1 with the…

Q: A : x +5 = y+7 93. B: z+6 = x + 3 %3D C: y+3 = z+ 4 cars/ min cars/ min 7 () B cars/min cars/min…

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Q: rs, and if c a and c| b, then c| (6

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Q: For how many positive integers 'n', n3-8n2 + 20n - 13 is a prime?

A: Introduction :

Q: Let n and r be integers such that n > 0 and 0 ≤ r ≤n. Prove that (²) ₁ = n (²-1) by counting in two…

A: Given, n and r be integers such that n>0 and 0<r<n.

Q: pls help asap!!!

A: According to guidelines we solve first three subparts when given multiple subparts.

Q: For the following claim Below you must disprove it. "For all integers x, x^2 + 1 is odd" Use the…

A: for example take x=3 .  then x^2 +1=10 , which is even.

Q: Let a, b and c be integers that satisfy 1 1 1 - - - - a b C |(A) 2022 (В) 2025 Find one possible…

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Q: Prove that 4 divides 6 7" - 2.3" for all integers n 20.

A: We need to prove that 4 divides 6.7n-2.3n for all integers n≥0.

Q: Explicit formula for an arithmetic formula an = a + (n - 1)d)

A: Explicit formula for an arithmetic formula is       an = a1 + (n-1)d  Where an is the value of the…

Q: G +n+3 ป for n= J 4n+l ******** โ

A: Here we have to state whether the given statement is true or false.

Q: 1.f a" da + C, for any real number n. n+1 O A. True ов. False

A: The solution is given below

Q: State Archimedean property of real numbers. Hence show that for each real number ɛ> 0, there exists…

A: We write the statement of Archimedean Property and proof the given statement

Q: + 1)32 – 120 000 = 2100(- how do you isolate for i?

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Q: The subject is DISCRETE MATH   Give a direct proof of the theorem “The sum of an even integer and…

A: Assume even and odd integers p and q respectively. Thus, p and q can be written as: p=2m and q=2n+1…

Q: 1. Prove that for all positive natural numbers n,13 + 23 + ... + n3 = n2⋅(n+1)2/4

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Q: (1123) x = (A3) 16. Find x!

A: Since the student has posted multiple questions and does not mention any specific question, so we…