If the repeating decimal 0.42424242 is written as an infinite geometric series, where a is the first term and r is the common ratio, then: O a = 0.01 and r = 0.42 O a = 0.42 and r 0.01 O a = 0.1 and r = 0.42 %3D O a = 0.42 and r = 0.1

Q: Determine the convergence or divergence of the series.

A: We have to find out            ∑n=0∞(1.075)n convergent or divergent

Q: Evaluate the geometric series or state that it diverges. 5.3k Σ k=3

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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: 9 n = 1

A: To find The common ratio from the given geometric series

Q: In  the given question as follows , find a geometric power series for the function, centered at 0,…

A: Given function is: fx=25-x We have to find the corresponding of f(x).

Q: Determine whether the given geometric series converges or diverges. If it converges, find its sum.…

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Q: Find S(6) for the geometric series with a=5 and r=10

A: To  Find S(6) for the geometric series with a=5 and r=10

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: Evaluate the telescoping series or enter DNE if it diverges. E 31 - 3 n+1 n=1

A: The solution of given problem is followed by

Q: (-1)" For the series En=1 n3 00

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Q: In the given question as folows , verify that the infinite series diverges:- see the  equation as…

A: given: ∑n=1∞nn+1

Q: find

A: The series is given as, ∑n=0∞n!k+6k+6n!xn The value of an is, an=n!k+6k+6n!xn The value of an+1 is,…

Q: Write an equivalent series with the index of summation beginning at n = 1.

A: Concept: Calculus involves the study of rate of change, which is used to calculate the objects which…

Q: S₄= 80/9 r (common ratio): 1/3

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Q: Which of the following series is a convergent Geometric series? 00 5 a) 1 080 b) O(1.05)" 00 c) O…

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Q: a se a geometric series to express the following repeating decimal: 0.234 234 234 234 234.…

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Q: Evaluate the geometric series or state that it diverges.

A: Consider the given series: ∑k=2∞3e-k We need to use ratio test to check the convergence of given…

Q: Approximate the sum of the series correct to within 0.00001. Σ (-1)" n8" n = 1

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Q: (a) For which numbers x does the geometric series E(3x – 2)" converge? (b) To what does the above…

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Q: Evaluate the geometric series or state that it diverges.

A: Known fact: ∑k=0∞xk=11-x  provided x<1.

Q: 00 (4-x)"· /n+5 9n · 7" n=1

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Q: state whether the series converges or diverges

A: Apply ratio test and check weather series is convergent or divergent.

Q: Find the first term for the geometric series described: Sn=484 an=324 r=3

A: Recall: Sum of the n-terms of the geometric series , Sn = a( 1-rn) /(1-r)    ; where a is the first…

Q: Determine whether the (-1) "3" 00 geometric series * is convergent or n=1 6" divergent, and if it is…

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Q: Write the first four terms of a power series with coefficients c9, c1, c2, and cz centered at 0.

A: Write the first four terms of a power series with coefficients c0,c1,c2, and c3.

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

A: Answer is convergent.

Q: Approximate the sum of the series correct to within 0.00001. (-1)" Σ n6" n = 1

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Q: Find the first term and the ratio between successive terms for the following geometric series. 1-…

A: The given geometric series 1-2y2+4y4-8y6+....... The first term and the ratio of geometric series…

Q: If the repeating decimal 0.132132132132 is written as an infinite geometric series, where is 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: Evaluate the telescoping series or enter DNE if it diverges. 00 E 3* - 3 n-1

A: The telescoping series is a special series such that when each term is decomposed, then, the new…

Q: Evaluate the geometric series or state that it diverges. 1 (-1)" n=0| 2n 2n

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Q: 3. Find the sum of the following geometric series or state that it diverges. 9 10 n=1

A: We have to find sum

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: Estimate the value of the sum of series, s = En 00 2n=0 (-1)" n! > to within an error of 0.0002.

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

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Q: Find the sum of the convergent series. 00 E on? + 3n - 2 n = 1

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Q: Determine whether this geometric series converges or diverges. If it converges, find its sum.…

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Q: Evaluate the geometric series or state that it diverges.

A: ∑k=0∞43-k=∑k=0∞34k On expanding, we get ∑k=0∞34k=1+34+342+343+.......

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

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Q: Determine the convergence radius and the convergence interval in each given series.. (a) ln(n+1) n+1

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Q: Find the sum of the following series correct to three decimal places. 3 n3 n=1

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Q: Find the value of the following convergent series: 10

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Q: Write S Σ as a telescoping series and find its sum. п(п-1) n=4 SN = S =

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Q: Evaluate the telescoping series or enter DNE if it diverges. 00 n=1

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Q: Find the sum of the series, if it converges. Otherwise, enter DNE. 20 Σ (-3)" 72 n=1

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Q: 00 10" Σ n-1 n=1

A: