x2 when x <1. Find a poweor series representation for 1+x3 O a. O b. E(-1)"x+2 C. O d. Ex3n +2

Q: 3. Determine whether the series n +1 3n2n n=1 converces or diverges.

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Q: 4. Find the sum of the following series: n=1 1 (a+n)(a+n+ 1)(a +n + 2) (a-n, n = N).

A: Introduction: The sequence of partial sums is very significant in determining the sum of an infinite…

Q: The sum of the series 1) is 1 n =1n+1 O A. -1 О в. 1 OC.O O D.1 O E. a 10 1/2 立

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Q: By writing the summation of the three power series E nCx" +EC„x"-2+ £G,"-, we obtaln: O None of them…

A: Here we will 1st convert every series in such manner that every one will have same power of x in…

Q: 9. Evaluate the following series: 7 (-1)^(6k) k=3

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Q: The first four nonzero terms of the series of 開51 A. 1+r+r + B. 1--1- 128 * C. 1-r+2² -r 1024 1 D.…

A: We will use the knowledge of Taylor series expansion and Taylor polynomials to find the first 4…

Q: 2 Find the sum of the first 20 terms of the arithmetic series 6 + 3 +0 – 3 – 6 – ..

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Q: 11) Find the sum of the series. 1 n(n + 3) Σ n=1

A: The given series is:  ∑n=1∞ 1n(n+3)

Q: C Find the Macdauin series of the function f(2)

A: A Maclaurin series is given by…

Q: Sum the following series: (a) cosa += cos(a +B) + COS (b) cos(na + B)+cos((n-1)a +2 2 (c) ·cos(α +…

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Q: n=3 (−1)n+1 22n+1

A: As per our guidelines we can only solve one question and rest of the question will be reposted.

Q: 1 3 (1+m²)²

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Q: 2" The value of p for the series En=1 by using ratio test is n! -1 O 8 2 0 ( 1 O

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Q: Which one is correct for the sum of the geometric series O O O 9 10 11 5 17 10 6 5 O Divergent Σ1…

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Q: 3. For what value of r does the series 1+r+r² + r³ + • = 10 ?

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Q: Find the sum of the series +.. = E (2n-12n+ 1) n=1 +] +.. + (2n-1X2n 1) O A1 O B.! O D. 0 ( series…

A: Series11.3+13.5+‐‐+12n-12n+1+‐‐‐         =∑n=1∞  12n-12n+1

Q: 2. Evaluate the series 2(n + 4). а. 26 b. 10 с. 16 d. -6

A: Given series is ∑n=14(n+4)

Q: Evaluate the series 7 E (n² – 5) n=1 44 O "Do You Want to Build a Snowman" -4 105

A: We have to evaluate the series: ∑n=17n2-5 Putting given values of n into the summation, we get…

Q: Find the sum of O 10 O 12 8 5 n=1 The series diverges. 573-2-n+1

A: Here we have to find the sum of the series.

Q: Which one is the sum of the geometric series 1 00 n= O 2 O 3 | 2 O Divergent 3/4

A: The sum of an infinite geometric series is given by, Sn=∑n=0∞arn=a1-r if r&lt;1 a is the first term…

Q: Find the limit of the series (if exist) 1 -1 3/4 1/4 4/3 1/3 None WI

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Q: find the sum of the series

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