converges, because 0 < 1 and an %3D debook 2n + 1 2n +1 2n +1 Room

Q: Use the ratio test or root test to decide if these are convergent or not: 00 Σ k 7k 5k k! k=1 k=1

A:

Q: If 2a, converges, then 1. diverges Select one: True False

A: Use the defination of convergence of a series.

Q: 3 converges conditionally because lim n - 3 = 0. 3n + 1 3n + 1 True False

A: The given question is solved with explanation below.

Q: Find the interval of convergence n!x" (2n)! n=

A: We have to check weather the given series is convergent or divergent.

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

A: Given is a series ∑n=1∞n2n+1n To check if the given series is convergent or divergent Ratio test:…

Q: Using Sandwich Theorem, the sequence 2 = 4 – - Cos2 n +1 n³ converges to 4 converges to 2 diverges…

A:

Q: this series converges or diverg 7n3 +19 Σ 2n2(4n +5) n=2

A:

Q: Find the interval of convergence of the series. (3x)" 2" n=1

A:

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

A:

Q: 2. Σ- n3D0 (n+1)4 If the series converges, use the Integral Test can be used to show convergence

A:

Q: Find the interval of convergence of Σ 6" (2n + 1)!

A:

Q: 10n2 + 18 Σ 7η2+ 16η+ 21 n=1

A:

Q: Find the radius of convergence for 2.4 6. ... · (2n) (2n)!

A: we have to find radius of convergence

Q: Determine whether En=1n converges or m%3D1 2n

A: Given: ∑n=1∞n2n

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

A:

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: Find all values of x for which ) (3x)" converges. n=D1

A:

Q: (3n)" (2n + 50)" n=1

A:

Q: What are all of the values of x ,such that - (-1) n+A converges? n=1 .1 X26 .2 06

A:

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

A:

Q: Use the ratio test or the root test to determine whether (-7)* converges absolutely or diverges. k2…

A:

Q: (3x – 4)* is - The radius of convergence of the series 9k k=0

A:

Q: (х+ 2)" nn n=1

A:

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: Find the interval of convergence: n³ (x + 5)" 6n n=1

A:

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

A: We can solve this as follows:

Q: If the infinite sum 7 k=2 k2 converges, use the Remainder Estimate to find lower and upper estimates…

A: Given ∑K=2∞1K72

Q: The interval of convergence of +∞ x2n Σ(-1)" is (2n)! n=0

A:

Q: 2 – 5n 11п-1 n=1

A: Use ratio test.

Q: Find the radius of convergence for 2 ·4 · 6 · ... · (2n) -x". (2n)! n=1

A:

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

A:

Q: Find the radius of convergence for: (2n)!æ" n=1

A: We will use direct formula for Radius of convergence without using ratio test

Q: Use the Limit Comparison Test to determine whether the series converges or diverges. 2n Σ n =1 5n2 +…

A: By limit comparison test, given series is divergent.

Q: Determine whether ∞∑n=1√n / 2n2+n+5 is convergent.

A:

Q: Suppose that p(æ) > anx" converges on (-1, 1], find the internal of convergence of p(6x – 9). n=0

A:

Q: If a power series ∞ n=0 anxn converges at some point x0 ∈ R,then it converges absolutely for any x…

A:

Q: Determine whether it is uniformly convergent £r20 x2+k2

A: Given  ∑K≥0xx2+k2

Q: the root test fails to determine if the series Σ (1 + n= 1 converges or diverges

A:

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

A:

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

A:

Q: Find the interval of convergence of ∞∑n=0 ((-1)n (x+1)n )/ (2n).

A: We have to find the interval of convergence of the given series.

Q: n· 3n 5n n=

A:

Q: 1dx x²+2x+5 -00 O diverges O None 37 converges to 4 converges to converges to converges to 3r

A:

Q: Use the Direct Comparison Test to determine the convergence or divergence of the s 5n Σ 4n - 1 n = 1…

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

Q: Show that 2"x" converges if |x| <. n=1

A:

Q: Find the values of p such that E(-1)"- converges.

A: The given series :

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

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!