diverges because an > 0. for all n 2 1. 2n + 1 True False

Q: The sum of any two integers of the from 4k + 1is always: Od Zero Even prime

A: Sum of two integers of the form 4k+1

Q: Let denote the n-th prime number. Show that Pn Pn n=1 diverges.

A: Divergence of the series

Q: Show that ø(n²) = nø(n) for every n E Z*.

A: I have used only one formula of euler phi function

Q: 3- Vn -) Σ Vn3 n=1

A:

Q: n! diverges because an > 0. for all n > 1. True False

A:

Q: Suppose an is conditionally convergent. Define what this means, and then use a proof by n=1…

A:

Q: converges, because 0 < 1 and an %3D debook 2n + 1 2n +1 2n +1 Room

A: We have to choose the true or false

Q: Verify by o Mathematical Induction dt todt E (2-1) = n²(2n²-1) for alt nz!

A:

Q: Find the term with no x in the expansion of x 15

A: we have to find the term with no x in the expansion of x3+12x-215.  as we know that the (r+1)th term…

Q: Prove by induction. 3F, = Fn+2+ Fn-2 for n > 2

A:

Q: (b) Show that k-1 (k+1) n n+1 for every n ≥ 1.

A:

Q: 1 Determine whether (-1)". converges conditionally, absolutely, or not at all. Vn2 + 1 n=0

A:

Q: Supposean converges conditionally (but not absolutely). Let A+ = {n €N : an ≥ 0} n=0 and A_ = {n € N…

A:

Q: Consider an = V4n2 + 3n – 2n for n 2 1. - (a) Determine if {an}, n=1 is convergent or divergent (b)…

A: Here, an=4n2+3n-2n, n≥1     =4n2+3n-2n4n2+3n+2n4n2+3n+2n     =4n2+3n-4n24n2+3n+2n     =3n4n2+3n+2n

Q: Show that > iP converges to a finite value iff p < –1. i=1

A:

Q: Show by example that Σ(an/bn) may diverge even though Σan and Σbn converge and no bn equals 0.

A:

Q: R² = gen gen

A: see below the reason

Q: Find all values of x for which ) (3x)" converges. n=D1

A:

Q: (b) Give an example to show that the product (fngn) may not converge uniformly.

A:

Q: O Determine whether En=1 st. converges or diverges. Justify your answer by citing a 3n+2

A:

Q: 4. Use the binomial theorem to find the first th ree terms in ascending powers of x of (1

A:

Q: Ahmet borrows n TL from Burak. Starting from today, Ahmet pays back to Burak 2 TL or 3 TL at each…

A: Given that Ahmet borrows n TL from Burak. Starting from today, Ahmet pays back to Burak 2 TL or 3 TL…

Q: converges to 0 Select one: O True O False

A: It is a series with increasing powers of π/3

Q: Proceed as in Example 3 in Section 6.1 to rewrite the głven expression using a single power serles…

A: Given ∑n=2∞nn−1cnxn−2+∑n=0∞cnxn+2 We have to rewrite the given expression using a single power…

Q: If 0 ≤ an ≤ bn and bn diverges, then an diverges. Select one: O True O False

A: This question is related to series and sequence, we will solve it using given information.

Q: Let ³ 10n 4n + 1 Determine whether is convergent.

A:

Q: 5. Prove that for all n n [j³ = j=1 n² (n + 1)² 4

A:

Q: Show that φ(n2) = nφ(n) for every n ∈ Z+.

A:

Q: . show that for every positive integer n, if n^2+2 is prime then n is a multuple of 3. Is the…

A:

Q: Use any method to deter (a) 13 The series 8.

A:

Q: Use the method of iteration to find a formula expressing sn as a function of n for the recurrence…

A:

Q: Determine the convergence or divergence

A: Consider the given series ∑n=1∞n2n4n3+1

Q: Suppose an is conditionally convergent. Define what this means, and then use a proof by n=1…

A:

Q: Determine if the given is convergent or divergent. I In"(n*) 23n2 n=1

A:

Q: Find f (n) when n = 2k, where f satisfies the recurrencerelation f (n) = 8f (n∕2) + n2 with f (1) =…

A:

Q: Dis cuss the Conditions For which Foun'er sevies is conv convergent ·

A: The objective is to show the conditions.

Q: 2. Show that for every n 2 2 and every 0 <k<n- 2, within the triangle of Binomial Coefficients k+2…

A: We will use properties of binomial coefficient  nCr  +  nCr-1=n+1Cr+1Note : nCr=nr=n!r! n-r!   Proof…

Q: Solve the recurrence relation subject to the basis step: S(1) = 1 S(n) = S(n-1) + (2n-1) for n ≥ 2

A:

Q: 은 hzl 3n+2 2n+3 h

A:

Q: IV. Determine if the given is convergent or divergent. s In"(n*) 23n2 #4. n=1

A: Given series is ∑n=1∞lnn(n4)23n2

Q: 1 is divergent. all n, then n=1

A: Given ∫0∞f(x)dx diverges∑n=1∞an convergent

Q: 1. Show that 2n n=0 onverges absolutely.

A: Given series: According to the ratio test:

Q: n! diverges because an > 0. for alln2 1. True False

A:

Q: Find f (n) when n = 2k, where f satisfies the recurrencerelation f (n) = f (n∕2) + 1 with f (1) = 1.

A:

Q: Given the expression an = V4n² + 3n – 2n for n > 1 Check whether this is convergent or divergent: an…

A: The given sequence is a an=Sqrt(4n2+3n) -2n.

Q: Expand the following recurrence to help you find a closed-form solution, and then use induction to…

A: Introduction: Every recurrence relation with prescribed initial condition has a solution that…

Q: (-1)"(7n + 1) Does En=1 converge or diverge? (3n + 1)

A: Alternating series test: If infinite series is If any of these two conditions does not hold, then…

Q: show that the sum of this: pi/(3sqrt(3))=(∑∞ n=0 ((-1)n (1/2)3n+1))/(3n+1) + ∑∞ n=0  ((-1)n…

A:

Q: . (a) Show that if a, is a series of nonnegative terms that diverges to o, then any

A: Answer :-

Q: 2" Σ diverges n=1n99 Select one: True False

A: We have to check

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.