Prove that by mathematically Induction. 2^n < (n + 1)!, for all integers n ≥ 2.

Q: Express f(=) = in a series of positive and (: – 1)(:– 3) negative powers of (: – 1) -

A: Given problem is :

Q: Use a direct proof to show that the sum of two odd integers is even.

A: Types of integers : Odd integers : The integer which is not divided by 2 . It has the form 2k+1…

Q: An theorem that specifies the complete expansion of a binomial raised to any positive integer power…

A: Complete expansion can be done by theorem

Q: Prove that Master Cheng has won precisely 21 times in a row during some consecutive days.

A: Please find the solution

Q: is diveugent 2) Show that the haronie series

A:

Q: When all the numbers in a given data series appear only once, then the series is said to: a. be…

A: We know that, Mode:     The value occurs with the highest frequency. Uni mode: When there is only…

Q: Determine the term involving y5 in the expansion of (3y +).

A: Please refer the attached image for complete solution. THANK YOU.

Q: Let (sn) be a sequence with lim sup sn = 10 and lim inf sn = 5. (a) Show that (sn) is bounded. (b)…

A: Consider a sequence, Sn, with lim sup Sn = 10 and lim inf Sn = 5. (a) To show that Sn is bounded. By…

Q: Suppose that {an}----->a, convergent real number sequence. Prove that {can}---->ca, for every c…

A: Suppose that {an}-----&gt;a, convergent real number sequence. Then, We have to prove that…

Q: Could you plz prove "upper reimn sum is always greater or to lower reimen sum"thanks

A: This question is related to reimann integration.

Q: Show that for any k > 3, any tree with a vertex of degreek must have at least k leaves. The proof…

A: Suppose there are l &lt; k leaves. The degree of each leaf is 1. Let there be n vertices. There is…

Q: Find a recurrence relation (with initial conditions) for the number of n-digit (n greater or equal…

A: Given:     The number of n digit ternary sequence without an occurrence of the substring 012.  A…

Q: Prove that the summation of three odd integers is odd.

A:

Q: Which positive integers less than 20 are relatively prime to 20?

A:

Q: Suppose n is an integer and consider the number n* – 6n³ – 18n² + 6n + 1. a) By expanding the…

A: Explanation: a. Given that,                    Expand the right side and show that both sides are…

Q: Let n and k be positive integers with 2k + 1 ≤ n. Find the number of ways to choose k children from…

A: Consider the given: Let n and k be positive integers with . Choose the number of ways in which k…

Q: How do we proof that 2logn = n?

A:

Q: Prove through mathematical induction that...

A: Mathematical induction is a method of proving a statement, formula, or expression. In this, the…

Q: Suppose that n is an integer such that n≥3. Using a combinatorial proof, show that:

A:

Q: Prove the z-transforms for common sequences summarized

A: So as per as our guidelines i am supposed to answer only 1 question please repost remaining part

Q: a) Proe by induction on n3, that 23"-/ is diwisible bu

A:

Q: An example of: Σ(an/bn) may diverge even though Σan and Σbn converge (show each step please)?

A: We have to show that Σ(an/bn) may diverge even though Σan and Σbn converge

Q: or an integer n>=3, an n-gon is an n-sided polygon. (example, a 3-gon is a triangle, 4-gon is a…

A: To prove: the sum of the interior anles of every polygon with n sides is n-2180° Now we shall take a…

Q: A ternary string is a sequence of 0's, 1's and 2's. Just like a bit string, but with three symbols.…

A:

Q: A knight on a chessboard can move one space horizontally (in either direction) and two spaces…

A: Consider the provided question, We have to proof: The knight can visit every square. Proof by…

Q: A positive integer n is called superperfect if ơ(ơ(n) = 2n Show that 16 is superperfect.

A:

Q: The sum of all positive integers less than 300 which are not divisible by 3.

A: Sum of n positive integer is given by, Sn=nn+12

Q: Suppose there is a currency which only uses 3-cent coins and 7-cent coins. Prove that for all…

A:

Q: Prove that a four-digit number is a multiple of 8 whenever the number formed by the first three…

A: The solution is given by using the expanded form of number as follows

Q: Find the recursion for a population that doubles in size every unit of time and that has 14…

A:

Q: Consider the following recursively defined sequence. fk = fk-1+ 24, for each integer k 2 2 f, = 1…

A:

Q: Hugh was trying to see if he could tile a 2" x 2" board with L-shaped tiles (i.e. a 2 X 2 tile with…

A: Given: We have given a 2n×2n board and we want to fit the board with L-shaped tiles such that ∃ an…

Q: 9. Let n be an odd number with exactly four distinct prime factors. If (3, n) = 1, prove that n is…

A: We will use knowledge of number theory to answer this question.

Q: sum of two even integers is even

A:

Q: If sequence a_n of positive numbers in increasing, then it is not bounded. TRUE or FALSE

A:

Q: Prove this Adams-Bashforth method using polynomial interpolation and prove it's second order…

A: As per the question  we have to derive the two-step Adams-Bashforth method by using polynomial…

Q: Define Permutation and Combination in your own wo

A: Permutation is a way to arrange the given objects or numbers in order .

Q: Write a recurrence relation that describes the sequence 1, 1,3, 3,5,5, 7,7,9,9, .... Don't forget to…

A: We will find out the required recurrence relation.

Q: Find the ordinary generating function for the sequence 0,0,0,0,1,1,1...(Hint: it is not a…

A: We need to find an ordinary generating function. The sequence is 0,0,0,0,1,1,1,.... Consider:…

Q: Please find a recursive formula (Using Stirling Numbers of the Second Kind.) for the number of…

A: Consider a partition 1, 2, 3, ..., n into k sets with n, k partition.  Let sn, k be the number of n,…

Q: : Use he comparism test to prove hat n-2 Converyes

A:

Q: Since the next prime after 7 is​ 11, the smallest composite number whose prime factors are all…

A:

Q: how that all the irrational numbers in the interval [0, 1] is dense there.

A:

Q: bn = /n In ( 1 + %3D

A: NOTE: Refresh your page if you can't see any equations. . the given sequence is  find the limit

Q: portion

A:

Q: Suppose that n students take a quiz and their scores sum to 150. What is the smallest number n to…

A: Pigeonhole Principle: The pigeonhole principle states that if n items are put into m containers with…

Q: Use mathematical induction to prove that for every integer n >=2, if a set S has n elements, then…

A: We have to prove that The given statement is for every integer n ≥ 2, if a set S has n elements.

Q: Fermat's theorem is not true for some prime number. اختر واحد

A: False

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.