What test is advisable if a series involves a factorial term?

Q: What is the sum of the series corresponding to sequence: 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9,…

A: We have to find sum of the series:

Q: The unemployment rates (%) of the four countries are as follows: 5, 8, 12, 20. What is the geometric…

A: The geometric mean of this simple series is, GM=x1×x2×⋯×xnn=5×8×12×204=96004=960014=9.8985

Q: Given the first three terms of a geometric series is shown below.  k , 6 , 5k+8 where ? is a…

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Q: 4. Study the convergence of the series In(1+ ) Inn n=2 and In(1+ ;) (In n)2 n=2

A: Observe the following inequality: 12n<1n+1≤ln1+1n for natural numbers , n≥2. ⇒1(2n) ln…

Q: Can the value of a series be determined using the Root Test or theRatio Test?

A: No, we cannot determine the value of the series using the root or ratio test. It can be only used to…

Q: Assuming the pattern continues, what is S₁2 for the series -8-15-22-29 -...? -565 -85 -510 O-558

A: Option d is correct.

Q: How can an elementary function be represented as a power series?

A: An elementary function can be represented by using Taylor series expansions. We use successive…

Q: Explain why careful analysis is required to determine the convergence or divergence of a series and…

A: Given: convergence and divergence of the series.

Q: Which of the series α) x − x³ + x6 − x¹0 + x¹5 b) X x² x3 xs .... are power series?

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Q: 6.25 1+z6 as a power series. 2. Using your answer in 1, write In |1 + x| as a power series. 1. Write

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Q: Evauate

A: Note: They cannot be integrated using the Binomial and Maclaurin series. It is solved by applying…

Q: Where does the subsequence series Nk = 2kpi come from? While I know it's used to specify the set of…

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Q: Choose the correct sum of the following geometric series Σο(!)" Option 2 O Option 4 O Option 1 O…

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Q: X = {1,2,5,5,5,8,4,6,7,5,9,6} the variance of the simple series is

A: Given information: The series X is given as: X = {1,2,5,5,5,8,4,6,7,5,9,6} Assuming that the series…

Q: Σ(;). Since the series can be rewritten in the form 4 a = r= it is a geometric series with:

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Q: An alternating series is one whose terms alternate between even and odd.

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Q: Which infinite geometric series diverges?   S=262+301.3+346.5+... S=6,651+729+81+...…

A: Infinite series.

Q: Find 81 term of series 41,43,45...

A: As we know that; The expression for the nth term of the arithmetic sequence is: Tn=a+n-1d Where, a…

Q: How does the convergence or divergence of a series affect the possibility of bounded summation?

A: The convergence or divergence of a series is closely related to the possibility of bounded…