Find a formula a, for the n-th term of the following sequence. Assume the series begins at n = 1. 1 1 1 8' 27 (Use symbolic notation and fractions where needed.) an =

Q: State what test you are using and show the given series satisfies the assumption for the test.…

A: ROOT TEST:    Let ∑n=1∞an  be the positive term series and let  limn→∞ ann= L.Then,…

Q: For Exercise, find the sum of the geometric series, if possible. SU 10 Σ 3/2)1 n=1

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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: Determine how many terms of the following convergent series must be summed to be sure that the…

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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: Find the sum of the following series na", |피 < 1 n=1

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Q: In  the given equation as folows , write an equivalent series with the index of summation beginning…

A: Definition used -                                   ∑n=0∞an=a0+∑n=1∞an

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

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Q: In  the given question as folows , find the values of x for which the series converges:- see the…

A: Rearrange and expand the series, ∑n=0∞3(x-4)n for n=0 and obtain 3+3∑n=1∞(x-4)n. ∑n=1∞(x-4)n is an…

Q: Given that T5 is a geometric series whose sum is 121 and has a base of 3, find its first term

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Q: E n(n – 1)c,x" – 2 – 9 n = 1 Σ - 9 E nc,x" + - n = 2 n = 0 8 8

A: Concept:

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: Find the sum of the finite geometric series by using the formula for Sn. 1 1--+ 4 16 64 256 1024…

A: Given problems:- Question 1     Question 2

Q: (х — 10)" 00 10" n=1 WI

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Q: Indicate whether the given series converges or diverges. If it converges, find its sum. 00 17) E Wik…

A: Solved below

Q: Find a formula b, for the n-th term of the following sequence. Assume the series begins at n = 1. 2…

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Q: Find the common ratio rof the geometric series a, that satisfies the following conditions: c = 4, S…

A: First I have written the formula of an infinite geometric series and then find the required…

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: Find the sum of the series to the accuracy IerrorI &lt; 0.001. How many terms of the sries do we…

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Q: In  the given equation as follows , write an equivalent series with the index of summation beginning…

A: The given series is ∑n=2∞ x3n-12n-1!. This implies that,

Q: The given series is convergent or divergent? 00 e¯n/3 n=1

A: Given query is to find series converges or diverges.

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: TT 80. E et+1 k=1

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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: If all the values in the series are the same, then what will be in relations to : A.M?  G.M?  H.M?

A: Arithmetic mean, geometric mean, and harmonic mean are the type of average. These averages are based…

Q: In the given equation as follows  write an equivalent series with the index of summation beginning…

A: The given infinite series is: ∑n=2∞x3n-12n-1! We have to write an equivalent series with the index…

Q: Determine how many terms of the following convergent series must be summed to be sure that the…

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Q: Find the sum of the series, if it converges. Otherwise, enter DNE. (VII)" n=0

A: We can write given series as: ∑n=0∞111n2∑n=0∞11-n2 It is an infinite geometric series with the first…

Q: For a given series, S1 = 1, S2 = 8, and S3 = 21. %3D %3D What is the 3rd term in the sequence? O 29…

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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: Determine if the series below converges or diverges. If it converges, determine what to do.

A: To discuss the convergence (or divergence) of the given series

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

A: Answer is convergent.

Q: For an as follows, write the sum as a geometric series of the form E ar". State whether the series…

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Q: use thE formula for the sum of a geometric series to find the sum or state that the series diverges

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Q: Find the sum of the series, if it converges. Otherwise, enter DNE. Σ (-8)"-1 n=1

A: We have to find sum

Q: Find the sum of the finite geometric series by using the formula for Sn. 1 1 1 4 1 1 1 1 1 - + + +…

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Q: Write the given decimal as an infinite series, then find the sum of the series, and finally, use the…

A: The sum of the infinite geometric series with first term a and common ratio r is given by…

Q: 1 How many terms of the series > would you need to add to find its sum to within 0.01? [n(In(n))®] n…

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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: For the series below, determine whether it converges absolutely, converges conditionally, or…

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Q: Find the sum, if it exists, of the given series: E (arctan(n?) – arctan(n + 1)*)) n=1 O 1 2 O -T T 4…

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

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Q: Find the values of x for which the series converges, then find the sum of the series for those…

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Q: The degree of the power series is а. 0 b. definite с. 00 d. none of these

A: I have given this answer in step-2.

Q: IM: 2. For each of the following series, determine if the series is geometric or not. If it IS…

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Q: Evaluate the series below. At what point will it converge? En! (x + 2)" n=0

A: Given ∑n=0∞n!(x+2)n

Q: Find the sum of the finite geometric series by using the formula for Sn 3 1 + 27 81 1 1 1 243 729…

A: To determine the sum of the finite geometric series given as: 1-13+19-127+181-1243+1729-12187. The…