(-1)"2"+1 is The sum of the series 5.9n n=1 -4 (a) 1+ (b) 5 1+ -2 (c) 5 1 -2 (d) 5 1+ -4 (e) 45 (f) None of the above. NI9 N/9 N/9

Q: 8. Find the sum of the series 5 if it exists. If no sum, write diverges on the blank provided. k=0…

A: Explanation of the answer is as follows

Q: 14. For the series Σn=1 (-1)" 3n0.3+8 S4= Include 4 decimals in your answer. Now find a bound for…

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Q: What is the sum of the infinite series 4 2n 37 ()* 37 2 2 1 +...+ (-1)" + (2n+1)! •• ? 3! 5! 7! O -1…

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Q: 2n+1 3) Rewrite the series with a new index of summation k so that k = n+1. (n+4)(n+1)

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Q: Find the sum of the first 20 terms of the series 10 + 6 + 2 +...

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Q: an is an infinite Series with Partial Sum SN=7-2 Syppose that 16 and 5. an what are the values of S…

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Q: n+7 9) Determine if the series E converges. Explain your conclusion. A Vn +n² -4

A: If limit n tends to infinity an /bn  exits and finite then an and bn converge and diverge together.

Q: Write out the first few terms of the series ∑n=0∞(1/3^n)+((−1)^n)/5^n. What is the​ series' sum? The…

A: Please see the explanation below

Q: 2(– 1)*+1 k(k + 10) By the alternating series test, the series converges. Find its sum. k=1

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Q: (i) Show that (r + 1)² (r + 2) – r² (r + 1) = (r + 1)(3r + 2). - (ii) Hence find (2 × 5) + (3 × 8) +…

A: Hi! You have posted multiple sub-parts. As per norms, we will be solving only three sub-parts. We…

Q: The sum of the series 3 (-k+1) is -k k-3

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Q: tion 1- ]: ): Determine whether the series 1 Σ (2n- 1)4 n=1 M8

A: According to guidelines we solve one question.

Q: [MO22] Express as a single power series form: 00 3. > (n – 2)an+1(2x – 3)*1+ An-1(2x – 3)"-1 n32

A:

Q: Find the sum of the series Σ 3n(x-3)n/(n+3)! from n=1 to infinity

A: To compute: ∑n=1∞3nx-3nn+3! ∑n=1∞3nx-3nn+3!=∑n=1∞3x-9nn+3!∑n=1∞3x-9nn+3!=∑n=1∞3x-9n+33x-93n+3!Shift…

Q: The series from n=5 to infinity of 5^n/6^n, find the sum of the series?

A: As we know that the sum of infinite G.P is given by, S∞=a+ar+ar2+...+∞=a1-r Where a is the first…

Q: If the power series a,a" converges only in the interval (-4,4), then the series n=0 nan converges…

A: .

Q: Find the first four terms of the binomial series for the function (1 + 10x) The first term is 1. 10x…

A: given,          1+10x13

Q: Find the sum of the series. e -8x² Σ (−1)n 87x6n n = 0 n! X

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Q: 39.The sum of the first n terms of a series is given by s = 5n² + 2n. The nth term of the serier…

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Q: 6 - Determine the value of the series n2+7n+12 * n-1 a)1 b) c)! d)? e)0

A: We have ,  ∑ n = 1∞ 1n2 + 7n + 12 Here , an = 1n2 + 7n + 12 We can factor denominator, an = 1n2 + 3n…

Q: [MO22] Express as a single power series form: >, (3n + 2)an-1(x + 2)n+3 – > (5n – 2)a,(x+ 2)²-1 n=-1…

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Q: What is the coefficient of x3 in the power series obtained in       -125/3   -25/3   25/3…

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Q: Express as a single power series form: Σ (3n + 2)an-1(x+ 2)n+3 – (5n - 2)а, (х + 2)"-1 | n=-1 n=3…

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Q: У (п — 2)аn+1 (2х — 3)"+1 + > aп-1(2х — 3)"-1 n=0 n=2

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Q: For the series (n+3), enter the first and the last term. n-1 First term = Last term

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Q: [MO22] Express as a single power series form: 00 (3n+2)an-1(x + 2)n+3 - Σ(5n - 2) an(x + 2)n-1 n=-1…

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Q: 15 sum of the series 3n-1X3nt 2)

A: We have to find sum

Q: (- 1)" Vrite out the first few terms of the series 2 4" n=0 What is the series' sum?

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Q: n' .2*+3 a) Determine whether the series 7*-2 converges or diverges. NT

A: Given: S=∑n=1∞n3.2n+37n-2

Q: Find the value of the series 00 1 k k=1 using the power series from Example 6. O In 2 O-In 2 O…

A: The solution are next step

Q: The sum of the series Zk=2 2e-k is e2-e O No sum 2e 1. e2-e O O

A:

Q: Write out the first few terms of the series ∑n=0∞((−1)^n)/5^n. What is the​ series' sum? The first…

A: Consider the series  ∑n=0∞−1n5n

Q: find the sum of the series ln(1-1/n^2) for n=2 to infinity

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Q: n=1 (Vn+5 Question Determine the sum of the telescoping series below. 00 9 Vn + 6 If the series…

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Q: (a) Find the sum of the series 4 – 3k+2 - 8k-1 k=0 (b) Find the value of r such that ) 3· r 2k+1 =…

A: For (a),     ∑k=0∞ 4-3k+28k+1=∑k=0∞ 48k+1-∑k=0∞ 3k+28k+1=4∑k=0∞ 18k+1-3∑k=0∞…

Q: (-1)' For the series calculate the sum of the first 3 terms, S3. 7n0.2 + 2 n=D1 S3 = Include several…

A: given series ∑n=1∞-1n7 n0.2+2

Q: 2n 3n + 1 Determine whether the series converges or diverges. Show all your work. 4 2n n=1

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Q: 5*+7)" 2" n=0 1. Find the values of x for which the series converges. Answer (in interval notation):…

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Q: -2 Find the sum of the series n=1 4n2+8n+3

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Q: 3. For the series 2 + 6 + 18 + 54 + etc., find; (i) the .... .. 12 term (ii) the sum of the first 19…

A: Question: for the series 2+6+18+54... Find 12 th term  Find the sum of 19th term

Q: 4. Find the x3 term of the power series X for the product of these power series Ex4 (A + Bx + Cx² +…

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Q: Express as a single power series form: У (Зп + 2)аn-1(х + 2)"+3 — У (5n - 2)а, (х + 2)"-1 n=-1 n=3…

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Q: 4· 8: 12•… • (4n) n = 1 R = Find the interval, I, of convergence of the series. (Enter your answer…

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Q: 4 – 3/k k2 - 2k k=3 the Integral Test be used for this series? Explain in detail your a

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Q: 4n²+5 + 2 n3 4. an 3. a, = %3D Vn3+1 5. What is the difference between a sequence and a series? 6.…

A: We have to solve given problems:

Q: 2n+3 5) Does the series converge or diverge? Provide a proof sequence as your answer. Make sure 5n+1…

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Q: (2) A series is said to be "alternating" if the signs of subsequent terms switch between positive…

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Q: 2n +1 Q1/ Find the sum of series 0 En- n2(n+1)

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Q: The sum of the series 2 3n-1 - 1 is given by n=1 6-1

A: Given series is an=3n-1-16n-1

Q: The series 4 + 12 + 36 + ·.· has no limiting sum because r > 1. Nevertheless, substitution into the…

A: Given series is