Suppose the repeating in 0.020020200202002.... continues forever. Is this number rational?

Q: Find the sum of the series. n=1

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Q: If the third term in the geometric series 2 ar" is 4 , then the product of the first five terms n =0…

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Q: Express the number ln(1.2) as a sum of an infinite series.

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Q: Find the Sum of the series 2/3 , 4/9, 8/27 .......to infinity

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Q: Use the geometric series formula 1 ∞ x³ 1 - = Σy to express the function as a series: n=0

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Q: Approximate the sum of the series correct to within 0.00001. (-1)" (4n)! n = 1

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Q: Give the first four nonzero terms of the series about x = 625 representing the function f(x) = v

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

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Q: For this arthmetic series, find S22 -6+(4)+(-2)+0+... to

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Q: The exact value of the series is discovered by /-

A: Consider the series

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

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Q: What is the sum of the finite series 19 Ë n=1 10n²+ 3n²2² 3 Give your answer exactly as an integer…

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Q: 9) Use your answer to the previous problem to evaluate the infinite series D ()". 100

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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: Try to use the geometric series formula to show that 1/9 is the same as 0.1111111111...

A: The sum of an infinite geometric series is given by S∞=a1-r and r must be less than 1. The given…

Q: Show that 0.222 is a rational number and find its value using geometric series

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Q: n of a series with its own lagged values is called

A: The correlation of a series with its own lagged value is called as autocorrelation

Q: The sum of the series Σ 1 is: 2" n=1

A: Given that: ∑n=1∞12n

Q: 4. use Geometric Series to find the fraction notation for: 0.55555...

A: Geometric Series is the series in which their is common ratio between all the elements of the…

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: Suppose that5. an is an infinite Series with Patial Sum 7-2 n:1 16 what are the values of S an and…

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Q: Find 21st term of series  12,16,18

A: n=21 tn=a+n-1d a=12, d=4 t21=12+204 t21=12+80

Q: can you please answer both questions. Decide whether those two series will converge. Thank you

A: Given series

Q: If it is known that limk00 ak = 0 , that is the kth term of a series goes to zero as k goes to…

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Q: The sum Sn of the first n terms of a series is given by S, ="(3n + 1). Show that the series is an…

A: we have to show that given sum of n term of series is an arithmetic series   According our…

Q: The power series x +......... can be expressed as 5 3

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Q: If an 3 what is the true about the series a,? 2"

A: Let we have given a series ∑an, we need to determine whether the series is convergent or not.Now…

Q: Evaluate ∫ e^−x2dx as an infinite series.

A: This question is based on indefinite integral.

Q: the first four terms to ximate the sum of the series:

A: Given,                ∑n=1∞1n2+1

Q: 2) Explain, in your own words, what it means for an infinite series to converge.

A: We have to explain the meaning of convergene of a infinite series.

Q: Write the general formula for following alternating series in the form An. n=1 10 10 10 + 9. 10 +..…

A: This is alternate series. Observe each term and find relation between them .

Q: If the third term in the geometric series 2 ar" is 4, then the product of the first five terms n = 0…

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Q: State whether the series for number 252 converges absolutely, conditionally, or not at all

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Q: Find the sum of the series. n! n- 0

A: Given series is ∑n=0∞-1n6nx2nn!                 (i) To find the sum of the given series (i).  Now,…

Q: Make up a geometric series Σarn-1 that converges to the number5 if a = 13/2.

A: Given:

Q: What is the exact value of the series from k=2 to 100 of (2/(k-1))-(2/(k+1))?

A: Distribute the sum with the two parts.

Q: By assuming solution as a series form

A: The given second order differential equation is x2d2y(x)dx2+xdy(x)dx+x2y(x)=0 Suppose a series…

Q: . Find the 31 st term of a series that has an nth term given by (10+2n)

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Q: Find the sum of the series. Σ 6"n! n = 0

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Q: (1+x)n

A: We can solve this as follows:

Q: Astudent argues that (-1)" /n is an alternating series and therefore converges. Is the student…

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Q: Find the sum of the series: n=0 x7n-6 n!

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Q: find the sum of the series 1 as a geometric series, differentiate both sides of express n=0 pect to…

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Q: Find the sum of the series: n! n=0

A: Given series ∑n=0∞x6n-3n! Let us rewrite the given series as follows ∑n=0∞x6n-3n!=∑n=0∞x6n.x-3n!…

Q: Find the sum of the series Σ 1/n(n+2) from n=1 to infinity

A: Given : ∑n=1∞1nn+2

Q: What is the sum of the series (1)/(n2-1) if n starts at 2 and goes to infinity?

A: To find the sum of the series  ∑n=2∞1n2-1

Q: Find the sum of the series. 8" n! n = 0

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Q: ++++s + +... 21 243 63

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Q: Approximate the sum of the series correct to within 0.00001. (-1)" (3n)! n = 1

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Q: Find the sum of the series Σ[1/n - 1/(n+1)]  from n=8 to infinity

A: Consider the following expression:…