Does the sequence xn ={n=1 converge in (0,1) ? why ? 100 %D

Q: Every power series converges at x=0. True or false.

A: Let us consider a power series with radius of convergence R, then interval of convergence of this…

Q: 1 vn Vn + 1, n=16

A:

Q: Find the sum of the convergent series. 1 (n + 1)(n + 2)

A: To expand the summation, split the given summation into the summation of two series.…

Q: Find the sum of the convergent series.

A:

Q: Find an upper bound for the error in using the sum of the first 8 terms to approximate the sum of…

A:

Q: The infinite series converges to L. By the use of the ratio test the value ofL will be ......

A: We have to solve given problem:

Q: Find the interval of convergence of the series. (3x)" 2" n=1

A:

Q: How many terms of the convergent series should be used to estimate its value with error at most…

A: Given series ∑n=1∞7n1.1.

Q: Sn(x) = e-(2-n)a

A: Given that, fnx=e-x-n2 To show that the given function is uniform convergence at [-1,1]. Let,…

Q: {()} Find the rate of convergence of the sequence sin as n=1 n 0 . n n 3 n4 1 n-

A:

Q: Find the interval of convergence of the series Ex-1 k=1 k3 *

A:

Q: Express the function as the sum of a power series and find the radius of 1- 3 convergence and…

A: Consider the provided question,

Q: 2 Σ e -n=1 In +1)

A:

Q: 2) is E=1 2n convergent?

A:

Q: The radius of convergence of the series 00 n! (3x – 1)" -

A:

Q: (x+1)* (+x) 3k k=0

A: Find the radius of convergence

Q: Suppose that the power series (2x-5)" converges conditionally when x = 5.5. What is its radius of…

A:

Q: Show that the series Σ (-1)"+1 log(n + 1) converges.

A:

Q: (3x – 4)* is - The radius of convergence of the series 9k k=0

A:

Q: Let fn(x) be the following sequence (not series) of functions n2 fn(x) = (x2 + 7x + 6)n² +n

A:

Q: Σ Show that n2 + 1 converges/diverges n

A: The given series is: ∑n=1∞nn2+1 Let  an=nn2+1,n≥1    =nn21+1n2   =1n1+1n2 And, bn=1n

Q: 42n (x + 6)" is convergent if The given power series : 9n

A: solve the following

Q: Find the interval of convergence and radius of convergence for the power series (2k) k=0

A:

Q: 00 k6 k! k=1

A: We have to apply the ratio test to the following series -  ∑k=1∞k6k!

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

A:

Q: 9. Estimate the value of the convergent series 8 k=1 (-1)^² k! + 2k with an absolute error less than…

A:

Q: What is the function represented by the power series from k=0 to infinity of ((-1)^k*x^(k+1))/4^k?

A: Power series

Q: Estimate the value of the following convergent series with an absolute error less than 10-3.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the sum of the convergent series. 2 [(0.9)" + (0.2)] n = 0

A: We have the given series as ∑n=0∞0.9n+0.2n Now, we have ∑n=0∞0.9n is a geometric series with a=1 and…

Q: 3n 4. Use the ratio test to determine whether Σ converges. (n + 1)! n=1

A: use the ratio test for convergence of series.

Q: Find the interval and radius of convergence for each power series. 3* x* (2k)! k=0

A:

Q: Estimate the value of the following convergent series with an absolute error less than 10 - 3 Σ…

A: Given

Q: Find the radius of convergence for: (2n)!æ" n=1

A: We will use direct formula for Radius of convergence without using ratio test

Q: Find the interval of convergence of the series (–1)"(x+3)*+1 п(п + 1) n=1

A:

Q: – 2n2 1+n² 2n²

A: Sequence is convergent.

Q: What is the convergency interval of (2n)l

A: The given series is,  ∑n=1∞n!23n2n!xn To find its interval of convergence.

Q: How many terms of the convergent series E1 (1/n'.1) should be used to estimate its value with error…

A:

Q: Find the values of the convergent series   [From n=3 to infinity] E(-1/3)^3n *that E is the sum…

A: The series can be expressed as follows.

Q: Find the interval and radius of convergence for the power series (3x + 5)k 2k k=1

A: ∑k=1∞ 3x+5k2k

Q: Find the sum of the convergent series. Σ 4 5 n = 0

A: Sum if given convergent series is 45.

Q: Use comparison test to show that the series E=1 (2) converges. 5n2-п.

A:

Q: The series C, (x + 6)" converges at x = -3 and diverges at x = -12. Based on this information, what…

A: Given series: ∑Cnx+6n converges at x=-3 and diverges at x=-12

Q: Find the rate of convergence of the sequence {(- 2 sin as n n=1 .n → o(:)° 1 n 1 n2 n3

A: Here we will find the rate of convergence,

Q: Let fn(x) be the following sequence (not series) of functions n2 fn(x) = (x2 + 7x + 6)n² +n

A:

Q: 1. Show that the sequence ((nx - - 1/n)e n) converges uniformly on [0, 0). (15 points)

A:

Q: Find the radius of convergence and interval of convergenc of the power series. 17. E (-1)"4" x" yn…

A:

Q: Find the radius of convergence for n! n=1 -xn nn

A:

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.