5. Let an be a power series with radius of convergence 2 and note that the constant term is 0. Show that there is a constant M so that for every x satisfying x ≤ 1. anx ≤ Mx|

Q: (-1)" V2n2 + 5 Given: power series > (x + 1)" n=1

A: Radius of convergence of a power series of the form ∑n=1∞anx-an  is given by R=limn→∞anan+1 For…

Q: Test for convergence/divergence, State the theorems used.

A: As per guidelines, I can answer only one question. Since questions are not interlink with each…

Q: find the interval of convergence.

A:

Q: (-3)" 2 3.5.7... (2n + 1) n=1

A:

Q: (X + 2)" 2) Find the interval of convergence for N! N

A:

Q: check if the fixed point itteration converge or diverge for  (6/x-5) in interval [4,5

A: f(x) = (6/x-5)

Q: Test for convergence the series 00 3.6.9 ... 3n (i) E x" (x > 0), 7.10.13 ... (3n + 4) 3D 0. 2.4.6…

A:

Q: tind the inderval of Conergence of the pacer Sevies nニ1

A:

Q: п(х — for -1)" n(x – 4)" 2n n3D0 8.

A:

Q: 3 xp- ² - 4 12

A:

Q: i) n=1 1 1+2+3++n j) 1 n In n(ln(Inn)+1) k) 2" +n n!+1 n=1

A:

Q: · (−1)″ √2n+ 5 n³ +2n +4 n=1 t) Å sin(n) 3 n

A: Given series are: s) ∑n=1∞-1n2n+5n3+2n+4                            t)  ∑n=1∞sinnn3 To prove: Test…

Q: (2r + 3)" =1' V 2n +n – 1

A:

Q: 19. 1 ntan-1 τη 20. Σ (-1)" n tan-1 in

A:

Q: スnX readius of convergence. the a.) Find b.) What is intervel et convergence? (Inter the

A:

Q: how do we find the radius of convergence for part b)

A:

Q: (X + 2)" 1) Find the interval of convergence for N!

A:

Q: 14. Find the interval and radius of converence for 3x √n+1 n=0

A: The given series is:∑n=0∞ (-3)nxnn+1

Q: Suppose that p(x)=an" converges on (-1, 1], find the interval of convergen n=0 8 left end included…

A:

Q: 27 n! n=0 converges to 0. 8.

A:

Q: en k%3D1 00

A: We will use Cauchy root test

Q: x" n n=0 n2

A:

Q: a) b) 1 2 3 + 2.2 3.2² 4.2³ 1 1 1 1 + + 1.3 2.4 3.5 4.6 + + 4 5 5.24 6.25 1 + n(n+2) + + +. 1…

A:

Q: (-1)"(n² /n +3) (х-5)" 2" (n° +2) 3 n=1

A:

Q: {au, ) IL x y² dx dy Q4-A) Show that the sequence B) Evaluate : ah (sinn)}, +sinh( converges to (1).

A: Given