3. (Cauchy condensation principle) positive numbers. do I xn n=1 Show that converges бирроге (хия й а if and only if decreasing 을 $ 2^x₂² n=1 requence of Converges

Q: What are all of the values of x ,such that E-1)n+1(n)* converges? x1.2 O x<1.30 x<0,40

A: By lebnitz test we observe n^x tends to inf gives zero only when x&lt;0.

Q: Use the power series g(x)= = ∞ 1 1 + x to find a power series for the function, centered at 0. 1 x +…

A: For all |x|&lt;R , given series is convergent and for |x|=R ,we need to check whether series is…

Q: Determine whether the following sequence converges, and if so, find its limit. (a) { (b) {n?e-2과)…

A: Sandwich theorem: If &lt;an&gt;, &lt;bn&gt; and&lt;cn&gt; are three sequences such that…

Q: What is the convergency interval of (-1)"-_(*-2)* 3-(2n+1) {(-)

A:

Q: 11 +4 Perform a test to determine if Tx converges. 1 11 X' + 4 Does T converge or diverge? 9 1…

A:

Q: (3) (0) Σ 10* k=0 2k

A: We have to find whether the given series is convergent or divergent.

Q: exmine if HS Convergent or divergent a) 2n²+3 8n7 7ntG

A:

Q: 3. Build a power series with the interval of convergence [-1, 9). (Note: There are many possible…

A:

Q: O4l determine if the geometric series converges o diverges o If seri es converg es, find its sum 3.…

A:

Q: (-1)"-1 (In n)" 00 23. E n=2

A:

Q: S(-19)" n! n = 1 absolutely convergent 8.

A:

Q: Find all the values of x such that the given series would converge. (-1)"(х")(п + 7) (4)" n=1 The…

A:

Q: Talyor series for f(x) about x = a is, f(m (a) f(x) = (x – a)" п! n=0 = f(a) + f'(a)(x – a) + f"(a)…

A: We find the Taylor series for f(x)=ex about x=0 and we also find the Taylor series for f(x)=ln(x)…

Q: An+1 Suppose limn→∞ = 3. Find the radius of convergence of 8. An an(-1)" En=0 -(x – 8)" ? 2"5

A: To find the radius of convergence of the given series

Q: n+1 D# 7 5(-1)"(x-5)" Find the radius of Convergence. 4" 1 4 с. d. 9. a. b. C.

A:

Q: n {(4)'} V3 The sequence {( converges. O True O False

A:

Q: 1 Ex '1.6.1 ) n-1 answer) 2n + 3u +5 reen Dapti converges absolutely Ex 11.6.2 (-1)" 272 3n2 +4 2n +…

A:

Q: If an diverges and 0 (-1)"an converges. n=1 B)>(-1)"b, converges. n=1 c) 2(-1)"bn diverges. n=1 D b,…

A:

Q: (-1)"n²(x+3)" 2. 5n n=1

A: Radius of convergence

Q: Evaluate an improper intergral. determine whether its convergent or divergent. 2 through infinity…

A:

Q: з Σ (-1)^ hai боu итиеть n ди

A:

Q: 10" An n!

A:

Q: Question 9. Let N = {1< x² + y² < 4, x < 0} be a domain in R². Use Green's Theorem to evaluate…

A: We have to evaluate the integral ∫x2y2dx+x3ydy using the Green's theorem over the region…

Q: of Eca 4 is cenvengend can we conclude that cach of these are convergent: (b) E cn (-4)^ ca)

A: Given that ∑n=0∞Cn4n is convergent.

Q: 9. The series 3k+ (k+1)* is Convergent Divergent

A: We will solve the following.

Q: true or false prove your answer Suppose that for every  ε > 0, the interval (4−ε, 4 +ε ) contains…

A:

Q: (x – 3)" which one are true? n=1 I: divergent for x = 5 II:Conditionally convergent for x = 2 III :…

A: 17. I. is true.

Q: 14. Divergent or convergent? If convergent, show the limit nsin(n) an n2 + 1

A:

Q: Find the interval of convergence for ΣΗ

A:

Q: 26. The interval of convergence for (X-3)* k - (x– is а. (-3, 3] b. [-3, 3] с. (-2, 4) d. [2, 4] е.…

A:

Q: Sin () fan--() absolutely Converyent, conditionally convergent E (-)" fonverget ardiver Calm or…

A: follow next step