Determine whether the given series is convergent or divergent. Justify your answers. +00 (2n)! 2(n + 1) 1 ( a) Σ (c) (-1)". 16n2 + 8n n=1 3 n=1 Inn (b) (-1)" n2 n=2

Q: (п +2)(х — 3)" Find the values of z for which the series2(-1)". п(n + 1)5" converges.

A:

Q: 3η2 +1 5. E - 00 =1 6η2-2n+ 3 6 Σ(-1)"+ 1 - + 00 2n n!

A:

Q: IV. Determine whether the given series is convergent or divergent. Justify your answers. 1 (2n)! (a)…

A: Note: Since you ask multiple question, only first question will be addressed here. It is given that,…

Q: 4. Determine if the infinite series diverges or converges. a. E2 b. En1 (n+1)2-1 3n+1 4n+2 C. c. E…

A:

Q: (4) Σ n=2 3n η3 x 5m (4)

A: Given series is then So we have Then from D'Alembert series test ,we conclude that given series is…

Q: Find the 81st term in the series defined by Sn= (n-3)²+ (n-5)²+ (n-7)² +(n-9)² +..

A: For this series, 1st term = (n-3)2 2nd term = (n-5)2 So like this nth term = [n-(2p+1)]2 So from…

Q: 3 (7) What is the value of the scries -? Justify your answer. (n + 1)2"||

A: Explanation of the answer is as follows

Q: Fex) =I_x-2) 나 - -n. + (-1)". (x-2)h 2 ht1 (x-2)? it Finde- a.values of (x) that make seriies…

A:

Q: Consider the series n=1 (2x)n n2

A: The objective of this question is to determine whether the given series converges or diverges for…

Q: Find the value of 7x²e-3 Determine whether ) (7n’e- ) n=1 Enter C if series is convergent, D if…

A: Let's find.

Q: Q3. Find the sum of the following series Σ 1 n2 n=1 4h

A: Solve the following

Q: n2 series E(-1)"+1- converges or n3 +1 n=1

A: Given

Q: 4. For each series determine if it is convergent or divergent. Give reasons for your answers. (-3)*…

A:

Q: The two series below are convergent (do not spend time testing for conver- gence). Find the value of…

A: Here we solve the given problem.

Q: Expand the function , in a power series E anx" with center c = 0. Find a„x". 8+7x n=0 (Express…

A:

Q: (-1)"2"+1 is The sum of the series 5.9n n=1 -4 (a) 1+ (b) 5 1+ -2 (c) 5 1 -2 (d) 5 1+ -4 (e) 45 (f)…

A: Find the value of series.

Q: Expand the function , in a power series E anx" with center c = 0. Find a,x". 2+3x n=0 (Express…

A: Explanation of the answer is as follows

Q: 7. Find the value of p for which the series >(-3)*(p – 5)" is convergent. n=1

A: This series will be convergent  if the  common  ration "r" will be less than 1.

Q: Rewrite the following expression En =2 n(n – 1)anx" +2 E=2 n(n – 1)anx"-2 + 3 E=1 100 n anx" as a…

A: Series expression problem....

Q: Find the sum of the geometric series for those x for which the series converges. Σ(-1)" (²-6)* 9 n=0

A:

Q: Find the sum of the following series. 00 (-1)" + 5n n=0 1 1 2/n 2/(n+1)/ n=1

A: In first part we have to use infinite sum of geometric series formula.

Q: Find the sum of the series 3n+1 (-1)7 n=0 OA. The series diverges by n-th Term Test T+3 В. C. T+ 3…

A: Expand the series and identify it than use the formula for the sum.