1 The series > n=1 (a) converges because lim 1 0. n-00 1 (b) diverges because lim 0. n-00 Vn (c) converges because it is a p-series with p = 1/2. (d) diverges because it is a p-series with p = 1/2.

Q: 1. Give an example of a series such that > an converges but > an| diverges.

A: To give an example for: ∑an converges but ∑ an diverges.

Q: S-1)"(x+2)" In 3" n=1

A:

Q: xn 00 Zn=1 1-3·5 ·...(2n-1)

A:

Q: 10. Find the interval of convergence and the radius of convergence of the power series - (x-4)" n-9"

A:

Q: Find the radius of convergence and interval of convergence of (-1)"4" the series. En=1 Vn %3D1

A:

Q: Determine convergence or divergence of the alternating series. (-2)h 5n6+ 2n n-1 Diverges Converges

A: Given, ∑n=1∞-2n5n6+2n In an alternating series to show it convergence in these two condition…

Q: Find the sum of the convergent series. Σ 2 3 n = 0 Determine the convergence or divergence of the…

A:

Q: Find the interval of convergence of the power series n 0 năa

A: Given :

Q: A power series representation of xsinhx2 is Σ-1). k=0 -(x+3)k is (k+ 1)! The interval of convergence…

A:

Q: Find the radius of convergence and interval of convergence of the series. E(-1)" (3n)! n=0

A:

Q: The geometric series (-5)* a) converges to 12 b) converges to 0. c) converges to - source was…

A:

Q: 6. Find the power series and determine the interval of convergence of 3x f(x): x2+x-2

A:

Q: Find the radius and interval of convergence for the power series Σ .( 2 3 n=1

A:

Q: Find the interval of convergence of the power series - 2)" | n =1 h

A: Given problem:-

Q: 3. Give an example of divergent series n=1dn and Ln=1 6n for which the series ("q + "p) converges.

A: Given: that An example of divergent series ∑n=1∞ an and ∑n=1∞ bn for which the series  ∑n=1∞ an+bn…

Q: 4) Find the interval of convergence for the power series F(-1)"-'n 2" t. n=1

A: Given series is ∑n = 1∞(-1)n-1n2nxn

Q: 6) Find the radius and interval of convergence for the series E0 (x+3" 'n%=2 (n-1)2"

A: Given: The series is ∑n=2∞ (x+3)n(n-1)*2n

Q: Suppose that the power series ) Cn(x – 1)" converges when x = -2 and diverges when n=0 x = 6. (a)…

A: The power series ∑n=0∞cnx-1n converges when x = -2 and diverges when x = 6. We have to find the…

Q: termine the radius of convergen ce for the power Series Ź Li)nt! (x-1)" n+1 -|x

A:

Q: Find the interval and radius of convergence of the power series (x – 5)k k2 k=1

A:

Q: (r- 3)" 2n +1 The power series £(-1)". has the radius of convergence R = 1. n=1

A:

Q: 13) Find the radius and interval of convergence of the power series (-2)" (x+3)" 3

A:

Q: The series > n=1 1 (a) converges because lim = 0. n0 Vn (b) diverges because lim = 0. (c) converges…

A:

Q: 2k k! k=0 8.

A:

Q: (-2)" 2n + 1 n=0

A: solution of the given problem is below...

Q: Find the radius of convergence and interval of convergence of the power series 2" (x – 3)" Vn + 3…

A: Solve the following

Q: Š (x-2)" n=1 3'

A:

Q: (-1)* Estimate the value of the convergent series with an absolute error less than 10-5. k! + 2 k=1

A: Solution is given below:

Q: 8. Find the second order derivative and interval of convergence of the series 1(x-3)2 1-(x – 3) +-…

A:

Q: Find the radius of convergence and interval of convergence of the power series: (x+3)2n+1 (-3)". 00…

A: Solution is given below:

Q: Find the interval and radius of convergence of the power series (x + 1)½ k=1

A:

Q: Find the interval of convergence for the power series =1 (x-1)" 7"n

A:

Q: 6. Find the interval of convergence for the series E - (x+4)" n-2" n=1

A:

Q: Find the interval of convergence of the power series (-1)"(n – 2) (x- 2)" n22" n=3

A:

Q: Give an example of two convergent series E1 *k and E1 Yk such that = *kYk diverges. Can this happen…

A:

Q: 6. Express the power series: >(-3)"(x)"-1 n=0 As a function. Then find its radius and interval of…

A: We can calculate radius of convergence by ratio test and then find interval of convergence

Q: 4 5. Find a power series representation of the function and its interval of convergence. f(x) 2x+3

A: we have to find  the power series representation of this function and its interval of  convergence

Q: 2. Find the radius and the interval of convergence of power series -(x + 1)"

A:

Q: The radius of convergence for the power series F(x-3)

A:

Q: Determine convergence or divergence of the alternating series. (-1)n n=1 5n3. Converges Diverges

A:

Q: 2. Find the radius and interval of convergence for the series. (x - 2)" nn n=1

A:

Q: 1 Using the fact that > x" = 1 + x + x² + |x| < 1, find a power series for the ... = - X n=0 2x…

A: We know that power series for a function f(x) is of the form f(x)= ∑n=0∞ anxnwhere an is coefficient…

Q: 3. 12. f(г) - 4 - х

A:

Q: 1. Determine whether the series ż 1 2n+1 1 2n-1) converges or diverges by examining the

A: Given series is ∑n=1∞12n+1-12n-1

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.