3. Show that 3.141592592592592... is a rational number, by expressing it as a ratio of two integers.

Q: Whenever n is a pOsitiv integer (n > 1). (15 points) %3D

A: Follow the procedure given below.

Q: show that the following number is rational by writing it as a ratio of two integers 5.6077

A: Rewrite the given number as: 5.6077 = 5+0.6077            = 5+607710000 only factors of 10000 are 5…

Q: Prove that the hundreds digit of n20 is even.

A: To Prove that the hundreds digit of n20 is even.

Q: Consider the following number. 0.59595959.. Show that the number is rational by writing it as a…

A:

Q: show that the following number is rational by writing it as a ratio of two integers. 2 9  +  2 3

A:

Q: Suppose the repeating in 0.020020200202002.... continues forever. Is this number rational?

A: We can not write the number 0.020020200202002... in the form  p/q where p is an integer and q is a…

Q: Show with the help of Fermat’s little theorem that if n is a positive integer, then 42 divides n7 −…

A:

Q: Show that the following number is rational by writing it as a ratio of two integers. 5.6057

A:

Q: The upper limit of the number of primes less than 23456 is O 2612 O 2331 O 5367 O 7136

A: Given number is 23456. We have to find number of primes less than 23456. formula for the number of…

Q: Show 2.5262626262626... is a rational number by expressing it as a ratio of two integers.

A: Show 2.526262626.... is a rational number by expressing it as a ratio of two integers as follows.

Q: 2. Prove that the number of irreducible fractions not greater than 1 and with denominator equal to n…

A: For the solution of the problem follow the next step.

Q: 3. Show that for any rational number r and any X>0, , In x= rln x'

A: The second fundamental theorem of calculus  (Newton Leibnitz formula) states that  : If h(x) and…

Q: 8. How many positive integers less than 1000 a) have exactly three decimal digits? b) have an odd…

A: According to our guideliness we can answer only the first 3 subparts. Positive integers less than…

Q: 2. The set of all rational numbers in the interval (0, 1).

A:

Q: 1. 0.0861861861861, when expressed as a rational number, is:

A:

Q: 9. This question is a little more challenging. How many integers in the interval [1, 99 999] (i.e.,…

A: Given data:   The given sum of all digits is k=10. The number of digits that can be used is n=5.…

Q: Show that the following number is rational by writing it as a ratio of two integers.…

A: Consider the given decimal number 52.4744174417441… Suppose that, x=52.4744174417441. Rewrite the…

Q: Suppose n ≥ 2 is an integer with the property that whenever a prime p divides n, p 2 also divides n…

A: let n=p1a1p2a2....pmam be the prime factorization of n  Here p1,p2....pm are all distinct primes and…

Q: 76. Find an exampie OI IWO irrational numbers a and b a for which a # b and is rational.

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Show that the following number is rational by writing it as a ratio of two integers.…

A: Given information: The rational number 52.4699169916991... Consider x=52.4699169916991...

Q: 9. Prove that V2 is an irrational number.

A:

Q: (1) Prove that is a, b, and c are integers with c + 0 then ac = bc = a = b ( that is this a key step…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Show that the following number is rational by writing it as a ratio of two integers. 0.74747474...

A: l

Q: Prove that between any two irrational numbers, there is an rational number via the argument of…

A: Given

Q: 2) express the given reapeating decimal as a fractional : 0.9999..., 0•159159159…, 0·782178217821… ,…

A:

Q: Show that the following decimals are Rational 0,444444444......

A: Show that the decimal 0.444444444...... is a  rational .

Q: show that the following number is rational by writing it as a ratio of two integers 0.74747474…

A: According to the given information, it is required to write the given number as a rational number.

Q: 2. Prove that V6 is irrational number.

A:

Q: 1. Prove that V3 is irrational number.

A:

Q: 3. Prove the following two theorems about pairs of "twin primes," p and (Recall that "twin primes"…

A:

Q: Show that there is no positive integer n for which In-1+ In+1 is rational.

A:

Q: prove that "The Sum of two odd numbers is even: using direct. Note:- 1 want the ansawer on a paper.

A: The sum of two odd numbers is even. Proof :          Properties odd and even integer.          If…

Q: Prove that the nth Fibonacci number fn≤αn−1, where α is the golden ratio.

A:

Q: prove that the one's digit of any integer,n, is the remainder when one divides n by 10.

A:

Q: Determine if 0.762050555854466... is rational or irrational and give a reason for your answer.

A: follow next step

Q: 1. 5.3535353, when expressed as a rational number, is:

A: we know the sum of infinite geometric  series  whose first term is  a and  whose common ratio is  r…

Q: Let N=20. Show using the Sieve of Eratosthenes how to find all prime numbers between 10N and 10N+100…

A:

Q: 6. Prove that if x is an irrational number and Y is a nonzero rational number, then xy is…

A: to prove this we take xy is rational number then show this is contradiction.

Q: 1. Show that 1105 is a Carmichael number.

A:

Q: Show that the following number is rational by writing it as a ratio of two integers. 2 +

A: Given                   29+25 So we know that rational number is in form of pqand where q is not…

Q: Find an irrational number between 5 and 9. 9.6767767776... 5.677      8.6767767776... 8.6 8.766

A:

Q: Prove or negate that there is a rational number x and an irrational number y such that x^y is…

A:

Q: E'v reR, 3 Cauchy sequence of rational numbers' such that an r

A:

Q: Let S be the set of all rational numbers that can be expressed as a repeating decimal in the form…

A:

Q: Show that the following number is rational by writing it as a ratio of two integers 0.79797979.

A: We have to write number 0.79797979... In the ratio of two integers . Lets=0.79797979...we can writ…

Q: 1. Prove that 3 is irrational number.

A:

Q: Decimals can be approximated by using only the leading nonzero digit or by rounding to the leading…

A: Answer : Approximate 0.0081 by using the leading nonzero digit = 8.1 × 10-3

Q: 1. Use Fermat's theorem to verify that 17 divides 11104 + 1.

A:

Q: Prove or disprove the following: n+1 For any odd integer n, H= ()) 2

A: Let  n=2k+1         -  (1) Where k is an integer. Then n is any odd integer. Now, LHS= n24        -…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.