(1) Show that n2 +1 n=1 converges conditionally. Show that all conditions of the test used are satisfied.

Q: E(- 1)n+ 1(n+1," converges conditionally n = 1 Select one: O True O False

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Q: Determine whether the following converges or diverges {(5) n 2n +1 n=1

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Q: a) Determine if Eº, absolutely converges, conditionally converges, or diverges. ´n=2 n-yn

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Q: The series Σ 6( − 1)*0.2-1.9/k○ diverges converges. k=0

A: We use ratio test to find the desired result.

Q: 5. Find the interval of convergence for the series f(x) = E· (-1)*(x-3)" (n+1)2

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Q: 4n + 3 Use the limit comparison test to determine whether > an = Σ 20n® + 2 converges or diverges.…

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Q: (-1)" Determine whether E1 converges absolutely, converges conditionally or stify your answer by…

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Q: What are all of the values of x ,such that Σ (3x)" (-1)"+ 00 converges? n=1

A: To solve this question we shall use root test for series.

Q: 1 Determine whether (-1)". converges conditionally, absolutely, or not at all. Vn2 + 1 n=0

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Q: +0 (2х — 1)" n V4n + 1 n=0

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Q: What are all of the values of x such that (-1)"+1 Σ (3)" converges?

A: The ratio test states that: if L < 1 then the series converges absolutely; if L > 1 then the…

Q: Determine whether the series 1/4 O 1/2 3/4 + Ex=1 ( 2² - 2 +²+1) 2k+1 0 1 converges and if so, find…

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Q: If C.)" converges, then C,)" converges. n=0 n=0 Select one: True False

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Q: 4 n"+ 1 then Converges 9) Dinerges Test Fails None of these

A: a) converges

Q: Suppose that dz converges. What can we conclude about the constant p? Op>1 Op Op< 3

A: Explanation of the answer is as follows

Q: a n+1) %3D 2n Ans. Converges, 6)

A: Since you have posted a multiple  question according to guildlines I will solve first (Q6) question…

Q: (b) Give an example to show that the product (fngn) may not converge uniformly.

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Q: (- 1)"+(- =D1 converges conditionally in elect one: True

A: Please refer to the image below

Q: If 2, =1ª, converges conditionally then E=|92| diverges 'n=D: Select one: True False

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Q: Exercise 2. Determine whether the sequence of functions (fn)n converges uniformly on S. fn(x) = nx"…

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Q: Σ Show that n2 + 1 converges/diverges n

A: The given series is: ∑n=1∞nn2+1 Let  an=nn2+1,n≥1    =nn21+1n2   =1n1+1n2 And, bn=1n

Q: Determine whether the given converges or diverges. n 2n +1 n=1

A: We can solve this as follows:

Q: 3. Determine whether E (-1)" converges absolutely, conditionally or diverges. Explain.

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Q: What are all of the values of x ,such that Σ.. (-1)" + 1 converges? (31)"

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Q: 5n – 1 8) Σ 7n n=1

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Q: Q3: Show that 3(2)n+2 3(2)n+2 is convergence and En=0 5n Zn=0 5n 20.

A: Please refer to the image below.

Q: 13. Determine whether ∞ Σ(-1)* k1/2 k=1 converges absolutely, converges conditionally, or diverges.

A: The given series,    ∑k=1∞-1kk12

Q: n2 + 5n + 2 Determine whether converges abso- (1+ )" lutely, converges conditionally, or diverges.…

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Q: Find the series' interval of convergence of (x* + * + })" x In(n) n2 n=3

A: Given series is ∑n=3∞x2+x+14nlnnn2.

Q: d) If Can's Converger and {b,'s diverges, Hhen fanton} Converges.

A: we argue by contradiction: suppose that an+bn converges. Since an converges by assumption, the…

Q: 1.2 Determine whether or not the series of functions {S„(x)} *-1} converges uniformly k=1 on [-a, a]…

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Q: 12. Use the ratio test to determine the values of x for which the power series x" Σ n! n=0 is…

A: We will solve the problem using D Albert's Ratio test.

Q: If E an converges, then an/n12 converges. n=1 n=1 O True False

A: True, using Abel's test.

Q: (-1)" In(n) Vn n=2

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Q: . Use the inegral test to show that =1 converges. 1+n2

A: To solve this question first we check derivative of function is negative for n&gt;0 and then we show…

Q: Find the interval of convergence of the series k(x+ 2)* 5k+1 k=1

A: The given series is: ∑k=1∞k(x+2)k5k+1...(1) Let, ak=k(x+2)k5k+1; k≥1

Q: Find the series' interval of convergence of (x² + x + })" In(n) n2 n=3

A: The given series is ∑n=3∞x2+x+14nlnnn2 We have to find the interval of convergence. Let…

Q: (4) Does the series (1+45 converge absolutely, converge conditionally, or does it diverge?. (6]

A: As per the company rule, we are supposed to solve one problem from a multiple problem set. Therefore…

Q: M Z(1-nsin-) converges n = 1 Select one: O True False

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Q: Suppose {fn}n=1 converges uniformly on E. Show {fn}n=1 converges pointwise on E.

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Q: 6. Determine whether the series (-1)"-'n-1/3 converges absolutely, conditionally, c n=1 diverges.

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Q: What are all of the values of x ,such that (-1)" -". 00 converges? n=1 x120 x0.4 0

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Q: ( 9n(n+1) (n – 1)!) n=1 A-Converges B-Diverges C- Absolutely converges D-Conditionally converges D O

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Q: 7n+2 5. By using Ratio Test, determine whether > converges or diverges. (n + 1)! n=1

A: The answer is found in step-2

Q: 5) Find all values of x for which En=1 nxn (n+1)(2x+1)n converges absolutely.

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Q: 4. Determine whether the scrics is absolutely convergent, conditionally convergent, or divergent. k…

A: Here we have, ∑k=1∞-1kkk3+2=∑k=1∞-1kak

Q: 3k 5- 2k+1 k=1 2 1. Does converge? If so, what does it converge to? If not, justify.

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Q: The series O True O False (-1)^ n Σn=1 is conditionally convergent.

A: Given a series ∑n=1∞an .  If ∑n=1∞an converges, but the corresponding series ∑n=1∞an  does not…

Q: The series (-1)"n²n! 2" n=1 O converges absolutely converges conditionally O diverges diverges…

A: Given series: ∑n=1∞-1nn2n!2nHere we have to check the correct option.

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.