43 divides 6^n

Q: Find the generating function for the sequence: 1-5,5,5,5 2-1,5,25,125,…………. 3-6,6,6,000,…

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Q: -, 1-, 3, 6, 12, 24 ...; find the 10th term and the sum of the first 10 terms.

A: The solution is given as

Q: Pigeonhole Principle Prove that among any 100 integers there always two whose difference is…

A: The given problem is to prove the following statement which follows the pigeonhole principle, we…

Q: Geometric Sequence: az = 72, a4 432, аg 3?

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Q: Find the Sum to infinity of the sea tès - Ce30 t ces 20 - 1-3 1-3.5 ces 30 + - (-nCBCIT). 2.4 2.4-6

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Q: A number N is divisible by 4 iff the number formed by the last 2 digits of N is divisible by 4. For…

A: We can find number divisible by 4  by using the concept given in the question

Q: Use sigma notation to write the sum.

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Q: Using sigma notation, write the expression -8 + 8 – 8 + 8 - 8 + 8+... as an infinite series in two…

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Q: 4. One way to add up n natural numbers can be described as: ("+1) which is in 'combinations' form.…

A: Generally sum of n natural numbers by using combinations we can find them using n+1c2. By using this…

Q: 1. Find the sum of all natural numbers having first term 1 and last term 303. 2. What is the sum of…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 20,31,45,62,82, use the method of successive differences to determine the next term in the sequence

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Q: What will be the sequence generated by the generating function 3x/(1-x)2?     a) 9, 12, 15, 18,……

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Q: Find the indicated term of the geometric sequence. 9th term of 1, - 1, 1, ... Enter the 9th term of…

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Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

A: Given- One of the term of the binomial expansion is 75x2y4. To determine- whether the statement…

Q: All composite number can represent as product of primes numbers

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Q: 15, 9,3, -3, how do you find the next term

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Q: Analyze the sequence 1, 8, 19, 105, 503, 1746, 4793, 11159, 23045, 43468, 76391 using sequences of…

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Q: 5. Describe four different rules for determining le next entries in the sequence that follows. Give…

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Q: Find Exponential Family 4-{N(0,1),0 € (-∞,+∞) }

A: Dear student, If you find this solution helpful please upvote ? it.   Here in this question it has…

Q: noosing a positive integer from 100 to 999, what is the poSSibility of choosing a positive integer…

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Q: Does a geometric sum always have a finite value?

A: Given :                  The geometric sum always have a finite value ?

Q: Determine the probability that the randomly selected number from the interval [0,1] is a rational…

A: To Determine: The probability that the randomly selected number from the interval [0,1] is a…

Q: Find the sum of the even integers between 35 and 49. The sum is ...

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Q: Express the sum in terms of summation notation. (Answers are not unique.)2 - 4 + 8 - 16 + 32 - 64

A: The sum of the series can be expressed in single term using summation notation . The summation…

Q: Use mathematical induction to prove: For each natural number n, 6 divides (n3-n). I need to write a…

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Q: How many terms of the series 54 , 51 , 48 ..... be taken so that thier sum is 513 ? Explain the…

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Q: What is the 100th term of a sequence of number in which, for every positive integer x, the sum of…

A: In the given question, concept of summation series is used. Summation Series The total of the series…

Q: 6. Describe four different rules for determining the next entries in the sequence that follows. Give…

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Q: Express the sum in terms of summation notation. (Answers are not unique.)3 + 8 + 13 + ....+ 463

A: Arithmetic progression is a sequence of numbers in which the difference between two consecutive…

Q: Find the indicated term of the geometric sequence. 9th term of 1, - 1, 1, . Enter the 9th term of…

A: nth term of geometric sequence is given by =an=a1rn-1 Where r=a2/a1

Q: We are given the continued fraction expansion for the square root of 89: [9; 2, 3, 3, 2, 18, 2, 3,…

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Q: 10, 15, 20, 25,30,35

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Q: 3. Multiply out writing the result in summation notation.

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Q: The first week, a patient engages in various exercies for 4 minutes every hour while awake. For each…

A: Explanation of the answer is as follows

Q: In two or more complete sentences, explain how to find the third term of the expansion of (2x+y)4.

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Q: Use summation notation to rewrite 15-3+3/5-...-3/625

A: A series represented in compact form is called summation notation.it is represent by the Greek…

Q: Fermat's theorem is true for only prime number. إختر واحداً.

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Q: How many twin primes are there where both primes are less than or equal to 31? Number of twin…

A: Twin prime: If there is only one composite number between two prime numbers, then that two numbers…

Q: A sequence a1, a2, a3,….. is defined by An+1 4аn — 3, п > 1 -- = k, where k is a positive integer.…

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Q: Find the sum of all  natural numbers between 250 and 1000 which are exactly divisible

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Q: 6th term of the series 12, 13, 17, ..

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Q: Decide whether the sequence 1, 2, 3, 4, 5, 6, 7,. is finite or infinite. ..... Choose the correct…

A: Given:      1 , 2 , 3 , 4 , 5 , 6 , 7 ........

Q: Serial numbers for a product are made using 3 letters followed by 2 numbers. If the letters are…

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Q: )In the sequence 2, 5 , 8, 11, 14, .. , the common, =) In the sequence 2, 5, 8, 11, 14, .. , the…

A: Given query is to find the value of indicated terms.

Q: Find the sum of the first 19 odd positive integers. Need Help? Read It

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Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: Given expression: 3c+c247 Concept used for the general term:…

Q: Explain how to write a formula to describe the sequence 1, 3, 9, 27, 81, 243, . Each term in the…

A: The given series can be written as, 1,3,9,27,81,243,.....  = 30,31,32,33,34,35, .... So, the given…

Q: Express the sum in terms of summation notation. (Answers are not unique.)

A: a0+a1x4+a2x8+----+a25x100 It can be written as,…

Q: en rectangl

A: Area of rectangle is  420 sq. cm Let the width the rectangle be w Therefore the length of rectangle…

Q: 8. Use a direct proof to show that the sum of two rational numbers is rational.

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