D. Test three of the following infinite sequence and series for convergence and give reasons for your answer: (n +5)! 1. {a, = 2n- Jan – n 5" 5!!n! n=1

Q: Justify the convergence of the general term numerical series: (- 1)" n? +1' n²+ 1 Where n is a…

A: consider nth term:

Q: Find the radius and interval of convergence of the series. (л — 2)" 6" In n n=2

A: Given series

Q: Tste for convergence of the series 1 En=2 (In (n))"

A:

Q: 5" (x- 2)" Σ (n + 1)! n=1

A:

Q: Q1) Which of the series converge, and which diverge? Give reasons for your answers. In(n²) 1) En=2…

A:

Q: Determine the convergence or divergence of the series

A:

Q: 5. Determine whether the following series converges or diverges, and prove your answer: n 2n-j n=1

A:

Q: n52n 10n+1* n=1

A:

Q: a. Investigate the convergence of the given series (2n + 1)! n²(n + 1)!" n=1

A:

Q: 1. Investigate the convergence and divergence of the following series, and obtain the sum upon…

A: We know

Q: What is the interval of convergence for the power series Š (x-1)", 3° n! n=1 A.(-00,00) B.(-1,1)…

A:

Q: - Test the convergence of the following series: 2" 6"/n n=2

A:

Q: b) Determine the convergence interval (with endpoints) of the following series: (x – 1)" 2"(n + 1)…

A:

Q: Find the interval of convergence for the given power series. n1°(x + 3)" Σ (4") (n#) 00 32 n=1

A: Given series is, ∑n=1∞n10(x+3)n4nn323

Q: Determine whether the series converges or diverges. 00 Σ n- 1 n4n n= 1

A: We have to check that given series is convergent or not.

Q: Which one is a conditionally convergent series? None of the given options is correct Ο Σ (-1)" n3 Σ…

A: We have find out from the given option which one is a conditionally convergent series.

Q: 8. (2x+5)" n! n=1

A:

Q: Q3/ Check the convergence of the following series 2 Σ 3(n + 1)(n + 2) n=0

A: According to our company guidelines if multiple questions are posted we can only answer one question…

Q: (x)2n-1 n3n n=1

A: Given the series ∑n=1∞(x)2n-1n 3n Let an = (x)2n-1n 3nan+1 = (x)2(n+1)-1(n+1)3n+1= (x)2n+1(n+1)3n+1…

Q: Decide the convergence or divergence of the following series. ∑∞n=1 1/(22n+1) and ∑∞n=1…

A:

Q: 00 (-1)" Ln-1 n п — n=2

A:

Q: Which of the series converge absolutely, which converge conditionally, and which diverge? Give…

A:

Q: 10. Find the radius of convergence and interval of convergence of the series 2"n²a". n=1

A:

Q: Determine the interval of convergence for the following series. 2 (X - 1)" 00 2-n 1- 2- n+1 'n%3D1

A:

Q: 1. Investigate the convergence and divergence of the following series, and obtain the sum upon…

A:

Q: (х — 3)" n2 n=1

A:

Q: 22. (z-a)", b>0 In n n=2

A:

Q: 8 .n X n n=1 n

A:

Q: Q1. Test for convergence of the following alternating series 00 Er-1"+1_n+1 E(-1)"+1 In +1 n=1

A:

Q: Q1. Test for convergence of the following alternating series In +1 n=1

A: We first check for divergence by using divergence test:  limn→∞an=limn→∞-1n+1n+1n+1…

Q: Determine whether the following series are convergent or divergent. 00 3 a. n + 1 n=1

A: Integral Test:      If f(x) is positive , decreasing and continuous function on [1,∞) such that…

Q: Determine convergence or divergence of the following series. n! n=1 2n

A:

Q: 28. Determine the convergence or divergence of the following series. Σ n =1 nn a. converges b.…

A:

Q: Decide the convergence or divergence of the following series. ∑∞n→1 1/(22n+1)      and    ∑∞n→1…

A:

Q: Determine the convergence or divergence of the series

A: We have the given series as ∑n=1∞lnn+1n Thus, limn→∞lnn+1n=limn→∞lnnn+1n=ln1+0=ln1=0 From the…

Q: est the convergence of the following series Σn=0 1 (-5)n

A: Ratio Test for Convergence: Let L=limn→∞an+1an A series ∑an converges if  L<1 and diverges if…

Q: el/n #5. E n = 1 n

A:

Q: 1 1) Show that the series N? converges/diverges. N2 N

A:

Q: 1. Determine the radius and interval of convergence for the following series n2x2n n! n=0

A: ∑n=0∞ n2x2nn!

Q: o 3(x+1)" En=1 n-4n

A:

Q: 00 Calculate the radius of convergence of the power series > n5"x" n=0

A: If r=limn→∞an+1an is less than one then its convergent and if r is greater than 1 then its…

Q: +∞ Σ n=1 (x + 1)n η n? + 1]

A: Given: an=x+1n3nn2+1 Now,           limn→∞an+1an=limn→∞x+1n+13n+1n+12+1x+1n3nn2+1…

Q: 1. Find the radius of convergence and interval of convergence for the following power series. n-1 00…

A:

Q: 3) Determines whether the following series are absolute convergent, conditionally convergent or…

A: here we will going to use two test  integral test for convergent /divergent  to check the series…

Q: Determine the interval of convergence of the given power series. +00 S(-2)"x" n=1

A: Given : Power series : an  To find : Interval of convergence Method using : Ratio test

Q: Which one of the following series is absolutely convergent? 4 E(-1)". n=1 n+ 5 00 6. E(-1)"-1 Vn +4…

A:

Q: 00 n! #1. Σ n =1 100" n' +1 Σ 2n #2. 2²+1 n = 1 #3. E1+ n n = 1

A:

Q: Q2/ Examine the convergence of the following series (n + 3)! 3! n! 3n n=1

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: