Find the centre and the radius of convergence for the power series Σ 13" (n + 22)® -(8x + 5)" 8 n = 0 (i) The centre of convergence is c= (ii) The radius of convergence is R=

Q: The series 33n 23n–2 is a geometric series. (1) What is its initial term a ? a = (ii) What is the…

A: a) To find the initial term we put n=1 Answer(a): 13.5

Q: 6x as a power series f(x) = >, cnx" 2 + x n=0

A: Given function is  f(x)= 6x/(2+x)

Q: (-1)"3" (4n + 2)2 п Find the interval of convergence for the power series >, n=0

A:

Q: (-1)"+1(2n + 3) n + 10 n=0 8.

A: ∑n=0∞ -1n+12n+3n+10 Apply Series Divergence Test If limn→∞an≠0 then ∑an diverges limn→∞…

Q: The squence is 1 + 4 + 16 + 64+ ... + 4^n. I know the common ratio is 4, and to use ((r^n) -1)/(r-1)…

A: Given series 1+4+16+64+....+4n      n+1 terms Therefore the first term is a=1 The common ratio is…

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: apply either the Alternating Series or Ratio Test To solve for these series

A:

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: Consider the series 00 (-1)" n=1 Use the drop-down menus to complete the following statement. 00 00…

A:

Q: Consider the series (-1)n*(3n2+n+5)/(4n3+2) = 5/2 - 3/2 + 19/32 - 7/22

A:

Q: Use the geometric series to derive a power series for the function f(x) = 1 / (1-x). What is the…

A:

Q: State where the power series is centered. Σ (−1)"(x – 7π)5η (5η)! n = 0

A:

Q: 7. Consider the power series (-1)*+lg" n+1 n2 n=1 (a) The series converges when |x| R. Find R. (b)…

A:

Q: State where the power series is centered. Σ Š (-1)"(x – 6x) 5n | n = 0 (5n)!

A: We use definition of centered of power series.