For which numbers ?does the geometric series converge? b. To what does the above series converge, for the numbers ? for which it converges?

Q: If the repeating decimal 0.42424242 is written as an infinite geometric series, where a is the first…

A: The given repeated decimal is: n=0.42424242 It can also be written as,…

Q: Write out the first few terms of the geometric series, > , to find a and r, and find the sum of the…

A: Given geometric series: ∑n=0∞3x-44n substituting n=0, 1, 2 , 3.. will give first term(a), second…

Q: Use the test of your choice to determine whether the following series converge.

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Q: Let Ean and Eb, be series with non-negative terms. If a, > b, for all n > 1 and b, converges, then…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Question No: 2 Find the radius and interval of convergence of the series En= 2n

A: To find Radius and interval of convergence of the given series.

Q: What is the radius of convergence of the series below if a = 12 and b = 8.

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Q: 5. Consider the geometric series (3x )" , determine for what values of x does the series n=0…

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Q: Find x such thatEx+2)-n = 4. (Hint: Use the formula for the sum of a geometric series.) n=0 X =

A: Series and sequence

Q: -What are all values of x for which the series

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Q: If the repeating decimal 0.42424242 is written as an infinite geometric series, where a is the first…

A: This question is based on Geometric progression.

Q: In  the given question as follows , approximate the sum of the series by using the first six terms:-…

A: The given sequence is ∑n=1∞(-1)n+12n3=∑n=1∞an Here an=(-1)n+12n3

Q: 4. For the series Σ=1+()", does it converge and if so what does it converge to? * n²

A: We have to check that series 1/2*(2/5)n  where n=1 to infinity. Is convergent or divergent.

Q: B. Given the series ...+ (i). For what values of x, does it converge? (ii). If you integrate the…

A: (i).  The given series is: 1-12(x-7)+14(x-7)2-.....+-12n(x-7)n+.... The given series is equivalent…

Q: Prove by induction the standard formula for the sum of the first n + 1 terms of a geometric series…

A: Consider a geometric series. If the first term is a and the common ratio is r, then n-th term of the…

Q: 27 81 Q4/ show that the following series is a geometric series ++ 46 100

A: Solution is provided below

Q: Find a formula for an for the nth term of the sequence  1/1, -1/8, 1/27, ... Assume the series…

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Q: une the radius and interval of convergence of the series 2 4...2n n=1

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Q: 3) Find the sum of the series (x-8) as a function of x on the domain, and say what the domain is.…

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Q: For what values of x does the series below converge? What is its sum? What series do you term by…

A: The given series is a power series and it is geometric  a+ar+ar2+ar3+....... a=1 the value of…

Q: Σ n" n! n=1

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Q: Find the nth term of the given infinite series for which n= 1, 2, 3, ... 1 1 +... 2x6 3x7 4x8 5x9 an…

A: Given 12×6-13×7+14×8-15×9+.....n is from 1,2,......... to infinity

Q: In the given question as follows , determine whether the statement is true or false. If it is false,…

A: Consider the given: ∑n=1∞n1000n+1=11000⋅∑n=1∞ nn+1 Apply divergence test and check weather series is…

Q: Determine how many terms are required to add to get within a 4 decimal place accuracy of the actual,…

A: The given series is ∑n=3∞-1n+115n. The given series can be rewritten as: ∑n=1∞-1n+115n+2 Clearly the…

Q: he convergence or divergence of the given series or state tha 1 10 n=

A: Answer is convergent.

Q: * 4" – 3" (a) If the series, converges, what is its sum? 5" n=0

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Q: For what real numbers q is the series below: absolutely convergent, conditionally convergent, and…

A: According to ratio test, if L<1, the series is convergent If L>1, the series is divergent If…

Q: n! n' n=1

A: The solution is given as

Q: Write out the first few terms of the geometric series. E to find a and r, and find the sum of the…

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Q: Find the next two terms of the series and determine whether or not the following infinite series…

A: The next two terms are 1/√5 and 1/√6

Q: Determine the sums of the following geometric series when they are convergent. 1. 1++ 2. 1+- (4) -…

A: 1) Given infinite geometric series: 1+16+162+163+164+... In given series first term is a=1 and…

Q: 53. For what values of x does the series 1 + (x – 3)? + -.. + (x – 3)" + ·. . converge? What is its…

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Q: Σ n=1

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Q: For each series, find an explicit formula for the sequence ofpartial sums and determine if the…

A: Given: The series ∑n=1∞1nn+1 To determine: The explicit formula for the sequence of partial sum and…

Q: For a, as follows, write the sum Sa, as a geometric series. 21 = 16 and dn+ 1 = -16 for n 2 1 n = 1…

A: We have, a1=116 And, anan+1=-16an+1an=-116an+1=-an16          ⋯⋯1

Q: 20. Find the sum, if it exists, of the infinite geometric series S =1+++ +.... O S= 3 OS= 2 O The…

A: Common ratio(r)  is obtained by the ratio of second term to the first term of the GP

Q: For each of the finite geometric series given below, indicate the number of terms in the sum and…

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Q: 4" – 3" a) If the series, E 5" converges, what is its sum? n=0

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Determine whether the following geometric series converges or diverges, and if it converges, find…

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Q: SW K=1 (-1)k k4 A. Har many terms must be Summed up?

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Q: Use the formula for the sum of an infinite geometric series to solve:A new factory in a small town…

A: A new factory in a small town has an annual payroll of $6 million. It is expected that 60% of this…

Q: Does the following series converge? If the series does converge, find the sum of the series. 4 ++ +…

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Q: S. =1+ 1 -+- 1 1 + +... - 00 4 9 16

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Q: Suppose Ea, and Eb, are series with positive terms and Eb, is known to be divergent. If a, > b, for…

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Q: For what Values of a B does the series 1 En=2 converge ? nº(In n)8

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Q: Let Ean and b, be series with non-negative terms. If a, 2 b, for all n >1 and Eb, converges, then a,…

A: We will prove or disprove the statement

Q: Show that the series is convergent. How many terms of the series do we need to add in order to find…

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Q: Find a formula for the general term an of the infinite series 1/3, 1/9, 1/27, 1/81+... Assume the…

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Q: Use any test to determine whether the series converges. 00 1 5) Σ (In 5)n n=1

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Q: 3. Determine whether each geometric series converges. If the series 7n+1 2n converges, find the sum.…

A: Let's find.

Q: For what real numbers q is the solution below: absolutely convergent, conditionally convergent, and…

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