If the series converges, find its limit. (Leave your answer exact.) If the series diverges, simply say "diverges". 1 1 А. 21/k 2* 21/(k+1) + 3* 4k 00 k=4 32 C. 1 - 34 36 +... 46 . 6! (2/5) + 42 . 2! 44 . 4! (2/5)? D. 1+ + 2/5 (2/5)4 + 2 3 4 B.

Q: 6. Σ. 4n² - 9 n=1

A:

Q: 2. Suppose thatEm=1an E bn two series, lim,cedn = L and a, s b, for all n. Then E1an and Ln%3D1 2n=1…

A: Explanation of the answer is as follows

Q: 4. Determine whether or not the series converges. State which test you use. 00 n- 2n2 + 1 n=1

A: We have to Check whether given series is convergent or divergent by Root Test.

Q: 5(- 1.8) is an alternating geometric series, which O divergesO converges. k 0 E5(- 1.8)*: | k=0…

A:

Q: Deter mine if the follo wing series are convergent or divergent. S u + 8n + an? 3+ 2n + n2

A:

Q: Find the function represented by the power series. 00 X+5 10 n= 0 10 O A. X-5 10 O B. x² - 5 10 C.…

A: Proceed as shown below

Q: Find the Generating function for the sequence 1,3,9,27,81,. Also find for which value the series…

A:

Q: 1+3* Does the series converge? If so, find the sum. If not, explain why. k=1

A:

Q: Example. Determine whether the following series converge or diverge 80 1 Σ(-1)k+1. √k² + k k=1

A: ∑k=1∞-1k+11k2+k

Q: 4. Which of the ff. series is convergent? 2 2 A. 6 – 2 + C. 1+ 2 + 3 + 4 +5 + . | ... 9. 27 Β. Σ 1…

A: A series ∑n=0∞an is said to be convergent if the sequence of partial sum sn=a0+a1+a2+...+an is…

Q: (b) Σ%1(-1)n+1 n2+5 n² +4 (b) Σ- (- 1)"+1

A: Alternating series.

Q: Choose any that is an arithmetic series. 4+8+12+16+...+200 50 Σ(1-2) j=5 45 Σ(12 + 3) j=1 45 Σ 3* K…

A: Here we have to choose the arithmetic series. A series is said to be arithmetic series if difference…

Q: Choose all that are geometric series. 109 E 3k k = 0 O 1000 x (1.2 + (1.2)² + (1.2)³ + (1.2)ª + ...…

A:

Q: Exercise 1.2A Identify the next shape in the series. 1. 2. 米 | ? | |3. -

A: We want to look for patterns.  Part(1) Let us first see the shape outside.  The first figure is…

Q: Find the sum of the arithmetic series by using a formula. 2+5+8+11+14+17+20 (Type the terms of your…

A:

Q: 1. Determine whether the sequence converges or diverges. "El

A: For a sequence ( an ) by perfoming ratio test limn→∞| an+1an | = r if r is definite number then…

Q: (- 1)"+(n+2) 1. Determine if the series Σ converges absolutely, converges conditionally, or…

A: here we have use the alternating series test if the series  is positive and monotone decreasing…

Q: Find the 8th term in the expansion of (2x - y)12. The sum of the first 20 terms of an arithmetic…

A:

Q: Q.4 - Determine whether the series converges, find its sum. converges or diverges. If it n=1

A: To determine whether the given series converges or diverges .  If it converges then to find the sum.…

Q: Find the sum of each series. Σ k=1 (k +1)(k +2) (a)

A: (a) The given series is ∑k=1∞2k+1k+2. This implies that, ∑k=1∞2k+1k+2=2∑k=1∞1k+1k+2=2…