(b) If f(x) = E anx", specify the domain of f. n=1 Based on your answer in Question 2(b), explain whether the series f(4) con- verges or diverges. (c)

Q: Determin tollowing series Convergence divergence. or り It zU

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: If 2 a, is convergent with positive terms n=1 is it true that sin (a,) is also n=1 convergent?…

A:

Q: 9) Σ=1 10) 3/3 - (-1)^(1+n²) n! 3 1 4 2 11) Σ.» (= − 1) =0 τη 13) Σ=1 14) En=1 15) En=1 Σ + n+1 12)…

A:

Q: For any positive integer n, prove that summation d divides n t(d)^(3) = ( summation d divides n t(d)…

A:

Q: Consider the following sequences n G In (1+n) (ii) e^/ (n²+1), (iii) √√n²+ √n²+2n -n. Which of the…

A: Let {an} be a sequence of real numbers If an≤an+1 ∀ n∈N then the sequence an is called monotonically…

Q: 1-x хр ха ес

A:

Q: gence of a sequence, prove that the following statements are true. (a) lim 2n+1 5n+4 nx (b) lim 2²…

A:

Q: Use initial value theorem and final value theorem to find f(0) and f(), if 6+7s2 + 5s F(s) s(s? + 4s…

A:

Q: 3-x -1 <x < 3

A: 63-x &lt; 1=&gt;  63-x &lt; 1=&gt; 63-x &lt; 1=&gt; 63-x×3-x  &lt;  1×3-x                   ∵ 3-x…

Q: lim (n22n) / n! = ?

A:

Q: 1 1 2n Σ (x – 3)2n-1 (х — 3) (х — 3)2я (x – 3) х — 3 n=| Σ Using the Fact : x" = , we get.. n=0 Σ…

A:

Q: The series 2n +2 Diverges to-o0 Converges to 1- Converges to B Diverges to +

A: Given series is ∑n=1∞sinπ2n-sinπ2n+2 The Nth partial sum of given series is…

Q: Expand the function f(x) into Fourier series: So T - I 0<r < -A<x < 0 f(z) =

A: In this question, we need to expand the given function into the Fourier series. For this first, we…

Q: Σ (-1)k (2k + 1)3(2k+1)/2 6 k=1

A: in thi question first we take series expansion of 1/(1+x²) then we do integrate with limit 0 to pi/6…

Q: To approximate Jio using N- what is the the Seg nence appropriate

A:

Q: 1 n³ + nªx²

A: