Q1. Test the convergence and divergence of ( 1. En=0 2. S0 (n+1)! %3D1 3n cosnn m%3D1 00 +. 3. Fo0 72 3!n!3n 4n-1 8. 210-Vn 6n2 6. En=1 n3+1 8. 7. 2n=0 n2+n+2 8. n=1

Q: Compute the limits of the sequences sin (n² – 3n + 7) n² +1 | 2n? +п -5 (b) b, (c) c, = n°e (а) а,…

A:

Q: Determine of each point convergens or diverges: (-1)"(31)/n! (n + 1)! (1)E (n+ 2)! n=0

A: As per the guidelines, I will solve only the first question. According to the limit comparison test,…

Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

A:

Q: What is the value of p = lim+¹ when applying the Ratio Test to assess n→∞an a convergence of? What…

A: Given problem:-

Q: 8. Investigate for convergence or divergence, and explain why (a) E) n=1 n (b) Š_n! 3n!–1 n=0 ( c)…

A:

Q: Q4. Test for convergences of the following , then find it's sum if convergence : X En=1 4n² –1…

A:

Q: Use a sum formula to find tan() 12

A:

Q: Which statement is TRUE? sin(n) diverges by n-th term Divergence Test. n=D1 n2 sin(n) converges…

A: Series problem....

Q: 6. Let f(n)= o(n)/n. (a) Show that if p is prime, then f(p) = f(p). (b) Find all n such that f(n) =…

A: Introduction: Euler's Totient function is a mathematical multiplicative function that counts the…

Q: * /In(n), cos?n COS n2 n=| Identify if it converges or diverges

A:

Q: 2) Determine the interval and radius of convergence of 2 '(x+5)** (2n +1)! 34n-1 n=0

A:

Q: Which of the following are convergent or divergent? Show your work. 72 i. En=2 lnn ii. En=1 3 1+ Vn…

A:

Q: converges or diverge 2n+ Sin(n)

A: The given series is  ∑n=1∞    12n+sinn We have to check whether the series converges or diverges.

Q: The first derivative of the power series 9 9x2 9x3 9x4 f(x)=9+ .. is 1! 2! 3! 4! O -9 f(x) O f(x)…

A:

Q: Determine the convergence of the integral tan r UTMUT dr. E (In(cos r))2

A:

Q: Let fn(x) = sin" x and let 8 > 0. a) Prove: fn converges uniformly on [0, 5 – 8], but not uniformly…

A: The given function is fnx=sinnx. To find: (a) fnx=sinnx uniformly or not on given domains.…

Q: 1. Test the convergence and divergence of 2. Σ (n+1)! 3!n!3n 6n² 6. Σ=1n3+1 7. Σ=0 210-√n n2+1+2 of…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: +o0 Зп? — 4 >Un where sn = u1 + u2 + · · · + Un 3n2 + 4 n=1 convergent O divergent

A: The given series is  ∑n=1∞un, where sn=u1+u2+⋯+un=3n2-43n2+4. We also, know the theorem that a…

Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

A:

Q: (4x – 12)" n=1 (-3)2+"(n² + 1)* - 3. Consider the power series (a) Determine the radius of…

A:

Q: SELECT ALI n! (2n – 1) A) converges by Divergence Test 2 B) a, = 1.3-5 ..... 2n C) diverges by…

A:

Q: determine the radius of convergence Σ n=1 η nn η ·(z — 2i)”. (n!) 5

A:

Q: n² (a) Show for all x E R, the sum E-1 COS converges uniformly. (b) Show for all x E R, the sum Ex=1…

A: Convergence of the series

Q: Prove that these two E E cos (Tin) não Inn 2 are تم 22=1 convergent (-1) h 22²41

A: A series is defined as the combination of the sequence. A series is said to be convergent when n…

Q: Use the comparison test to determine convergence or divergence of 00 cos² 3n Note that 0 ≤ Σ n=1 1+…

A: In the comparison test, we compare a series ∑un with a series ∑vn, where we know the convergence or…

Q: 5). Find the interval of convergence. ∞ n = 0 xn n7 + 8

A: Introduction: A power series can either be convergent everywhere or can be convergent over a…

Q: Q6. (1) Given log(1+t) = t = t + t² 4 valid for 1411, determine the power. series for log (1+2x) up…

A:

Q: determine the radius and convergence of E n=1 5xn/3n2

A:

Q: ach problem, test for convergence or divergence: 1 n=1 n\n 1 (n +1Xn+2) 2n+3 n=1 n² +3n + 2 n-1 n=1

A: