5+ 2an 5) A sequence an is defined by a1 = 1 and n 2 1. Show that an converges, and find its limit. An+1 %3D 4

Q: Euclid of Alexandria is credited with writing a series of 13 mathematics books called The Elements…

A:

Q: Pascal's Triangle 1 1 2 [ 3 ] 1 6 I4I1 15 I 10 I 10 I 5[1 I 6 I 15 I 20 I 15I 6I 1 [7 [21 [35[ 35 I…

A: Answer

Q: (b) Prove that 1(1!) + 2(2!) + 3(3!) + for all positive integers n. ... + n(n!) = (n + 1)! - 1

A:

Q: Find all of the 5-th roots of the number z Show all of your working! -√3+i. ==

A: We have to find all of the 5-th roots of the numberz = -  + iWe know that, Polar Form of a Complex…

Q: 2 proofs of binomial identities applied to Pell-Lucas numbers.

A: The Pell-Lucas numbers are a sequence of integers defined by the recurrence relation: P(n) = 2P(n-1)…

Q: Show how James Garfield (1831-1881) proved Pythagorean Theorem

A:

Q: 2. Ifr + 1, show that for any positive integer n, a + ar + ar +...+ ar" = a(rn+1 – 1) - r - 1 the…

A: we need to prove if r≠1 thena+ar+ar2+.....+arn=arn+1-1r-1let pn=a+ar+ar2+.....+arnto prove…

Q: We assume that x0. Therefore there exists a natural number n such that n> Since z is fixed we can…

A: Suppose that x and y are 2 distinct real numbers. We have to prove that, there exists a rational…

Q: (A-B)nC= A – (BŪC) as above None of these (BUC) – A A- (CUB) as above as above:

A: A-B∩CUse venn diagram to find the answer,

Q: I really only need the highlighted part explained, if you could explain how they take the steps as…

A:

Q: Can you show its proof by using contradiction?

A: As per the question we are given a vector space V = {f | f : R → R} of real functions of a single…

Q: Question: x"- 6x +9 く9

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

Q: From all three-digit numbers find the one tha

A:

Q: 9 – i 3 + 9i If A = find A*. 7+ 5i -4 + 8i ( ) ? ? ? ? A*

A:

Q: Theorem 1. For every prime p, /p is irrational. Proof. Write your proof here... Theorem 2. Let a, b,…

A: NOTE:- By bartleby rules, only first question is answered To prove that for every prime p, p is…

Q: Using the Root Test 12. (in (² + 4))***

A:

Q: How is this done with proof by contardiction?

A:

Q: To continue the proof by induction, begin with 4 + 16 +64 ++4 OA. 4-1 0 в. 4к OC. 4k+1 OD. 4K-1 Add…

A: Principle of mathematical induction: If P(n) be a statement and n is natural number.  Step 1: Verify…

Q: For this question can you explain how proved it to be transitive? As don't understand the last part…

A:

Q: Click and drag the steps to show that at least three of any 25 days chosen must fall in the same…

A: In discrete mathematics, there are two basic methods for proving a statement is true: proof by…

Q: TT IT 14) Find the rule for the table -2 15) Find the rule for the table -11 1 -2 -1 -1 -6 3 -1 1 4…

A:

Q: I need to do a table proof and I don't know what theorems and postulate to use for this. Will I…

A: Similar triangle property

Q: Evaluate - DI 2 x (√Vin(4-x²)).

A:

Q: Non-Calculator Find the extrema by a) finding critical numbers, b) setting up a sign line, and c)…

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

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT How many positive integers n ≤ 1000 are coprime with N=90

A: We know that 90=2×32×5 Numbers less than 1000 which are divisible by 2 =10002=500 Numbers less than…

Q: Find all of the 5th roots of the number z = −√3 + i. Show all of your working

A:

Q: Use a random number generator to generate 50 values between zero and one (inclusive). List them in…

A: Note: Hi there! Thank you for posting the question. As there are multiple several questions,…

Q: A student invented a drug to regulate, specifically to decrease, the blood sugar levels of people…

A: The data given represents sugar levels of a person before and after taking the drug. Each sample has…

Q: 3. Explain the relationship among the three concepts: well ordered principle, induction, strong…

A: We know. Well ordered principle:  A set of numbers is known as well ordered when each of its…

Q: Use Excel to find the regression line, the correlation coeffient r and the coefficient of…

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

Q: Question 27. If x > 0, then x+

A:

Q: Find the value of cif Σ (1 + c)=^= 1 n=2

A:

Q: Prove that if PQ≅RS and RS≅UV then PQ≅UV in the simplest way possible. Please do not use any example…

A: Congruent relation is an equivalence relation. So, congruent relation is a reflexive, symmetric and…

Q: Question 28. If a is an integer and a? | a, then a E {-1,0, 1}.

A:

Q: You are provided with 15 and 20 cent notes. Show using strong induc- tion that all amount that are…

A: Given: Let us consider based on the given data that Sk = 5k and be S1 = 5. Because given that all…

Q: 2) (a) Find all integer solutions to the equation 161x + 71y =1. (b) Find all integer solutions to…

A:

Q: =] Verify n(n + 1)(2n + 1) 6 j=1

A:

Q: the answer that is provided is not correct all of them except number 1. Can you please try to do it…

A:

Q: 6479x + 1053y = 4.

A: Calculating GCD(6479,1053) gives: 1053 = 0*6479 + 1053 6479 = 6*1053 + 161 1053 = 6*161 + 87 161 =…

Q: The set of all upper triangular n x n matrices is a subspace W of Mnxn(F).Find a basis for W. What…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.