Q.2. Calculate the first 8 terms of the sequence of the partial sums correct to 4 decimal places. Does the series appear to converge of diverge based on your calculations? n² (a). Ln=1 n+1

Q: Find the sum of the following convergent series. 1 b. 2n=122n-1 1 e 2n+1 (

A: The solution is :

Q: Consider the series E=1 k+11 k+12, (a) List the nth term, sn , of the sequence of partial sums for…

A:

Q: 3. Give an example of a convergent series Exn and a divergent series Eyn Ssuch that E(xn + yn) is…

A: Let ∑ xn be a convergent series and ∑ yn be a divergent series

Q: Find the sum of the convergent geometric series: En=0 (3n+1 4n+1

A: We have to find the ∑n=0∞3n+14n+1=?

Q: 30. Suppose that E-o Cnx" converges when x when x = 6. What can be said about the convergence or…

A: We have the given series is ∑n=0∞cnxn is convergent for x=-4 and divergent when x=6. Let R be the…

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

A:

Q: Find the radius of convergence of the power series E n+ 1 (x – 3)". 3"

A: To calculate the radius of convergence of a power series, apply the ratio test. If , then the…

Q: Find the values of x for which the series converges. E(-3)"x" n = 1

A:

Q: Find the sum of the convergent series. 6. Σ 9n2 + 3n - 2 n = 1

A:

Q: 2. Determine and justify whether Σ-υ i=1 is convergent or divergent. If it is convergent, give the…

A:

Q: Find the interval of convergence of the power series -(x + 3)³n . n=1 n 27"

A:

Q: Find the interval and radius of convergence of the power series E(-1)** (x+2)" п 2" n=1

A:

Q: 1. Find positive value of p for which the 3. series converges. 25 n=1 p

A: Given:Given that an=3pnTo find:we find the value of p for which the series converges.

Q: 2. Verify that the infinite series converges 00 п a) E (:)" 6 n=0 00 n b) Σ-0. 6" n=0

A:

Q: Find the values of x for which the series converges. Σ n=0

A:

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: 1 1 + 2y2 1 1 + 4V4 + 3/3 5V5 +

A: We will test the convergence of given sequence by using p-series test as shown below

Q: Find the sum of the convergent series. +0 | 3n+1 6n-1 n=0

A:

Q: Find the radius of convergence and interval of convergence of the series. "+4 5n! n=2 R = I =[( +)-

A: We have to find R and I .

Q: Calculate the first three partial sums of the series. S₁ S N' 11 = S3 = Σ n = 1 n+4 Use the sequence…

A:

Q: What is the smallest value N for which we can guarantee that the error approximation of the…

A: Given series is  which is convergent alternating series as the sequence {1/(n^2+2n)} is decreasing…

Q: 22. Find the sum of the convergent series. 10 " 11 n=0 a. 20 h 24

A: Solution of the problem as follows

Q: Find the sum of the convergent series.

A:

Q: The series k=1 5( − 1)k+1 - kl.1 O converges diverges.

A:

Q: 19. Find an upper bound for the error in using the sum of the first 8 terms to approximate the sum…

A:

Q: For the following alternating series, an =1- 2! (0.5)2 (0.5)4 (0.5) (0.5) 4! 6! 8! how many terms do…

A: Here convergent alternating series is, ∑n=1∞an=1-(0.5)22!+(0.5)44!-(0.5)66!+(0.5)88!-... and…

Q: Suppose the series a; has a sequence of partial sums given by sn = 1+ n²–1 2n2+3' Determine i=1 if…

A: Given that ∑i=1∞ai has a sequence of partial sum as sn=1+n2-12n2+3. A series converges means its…

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

A:

Q: For the following alternating series, (0.6)7 +... 7! (0.6)3 (0.6)5 An 0.6 - 3! 5! n=1 how many terms…

A: Given:   Alternating series is given

Q: 2. ∞ Σ Find the sum of the convergent series: n=1 1 4n2 –1

A: Find the sum of the convergent series 1/(4n2-1) from n= 1 to infinity.

Q: Compute the general term an of the series with the partial sum Sn = 2 n + 2 , п> 0. 2" %3| - An =

A:

Q: ind the sum of the convergent series. +00 3n+1 Z 6n-1 n=0

A:

Q: find the first 6 partial sums for the series; does it appear to converge? If so, find the sum.

A:

Q: 1. Find the radius and interval of convergence for the power series (-1)" (x – 1)*". 2n n · 9n n=1

A:

Q: Suppose you are told that the sequence (Sn) of partial sums of a series with positive terms…

A:

Q: Find the sum of the following convergent series. 3n+1 1 6n-1 n=0 'n + 1 n=16

A:

Q: n + 2 2- Compute the general term an of the series with the partial sum Sn -,n > 0. 2" an If the…

A: Here we have to compute the general term an of the series with the partial sum        Sn = 2 -…

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: Find the interval and radius of convergence of the power series k -(x – 2)* 42k 1 k 1

A:

Q: Determine the radius of convergence of the power series. E kl(x - 4)K k= 0

A:

Q: For what values of $x$ is the series $\sum_{n=0}^{\infty} n ! x^{n}$ convergent?

A: Given the series is We have to calculate the value of x for which the given series is convergent.

Q: Find the sum of the convergent series: > (e1/(2n-1) – e1/(2n+1)) n=1

A:

Q: Find the sum of the convergent series.

A: Sum of Geometric series: ∑n=0∞arn=a1-r Where a is the first term and r is the common ratio.

Q: Determine the radius of convergence for the power series E k:(x – 49)*. k= 0

A:

Q: . Find the sum of the following convergent series. Σ 00 3n+1 a. 6n-1 n=0

A:

Q: 21. Find the sum of the convergent series. n =0

A: ∑n=0∞434n We can simplify, = ∑n=0∞22.2-2n3n = ∑n=0∞22-2n3n =4∑n=0∞2-2n3n  = 4∑n=0∞34n

Q: Find the radius of convergence and interval of convergencE of the power series. (x 25. E 2)" n=1 n"

A:

Q: Evaluate E-2(1/(k² – 1)) by finding the limits as n→o of the series' nth partial sum.

A:

Q: Σ (-1)"+12"(x+1)" n3n n=1

A:

Q: For what values of p does the series converge (initial kP k=10 index is 10)? For what values of p…

A: Given infinite series is:

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.