For any positive number a, prove that the series Ek=1 k converges.

Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say…

A:

Q: Consider the real sequence {an} given by an = In(n+ 1) – In(n + 2), ne Z20 = NU {0}. Justify whether…

A: Given :  The sequence an given by ;              an = lnn+1 - lnn+2  ;    n≥1 To find :  To check…

Q: Find the positive values of p for which the series converges.

A:

Q: For what values of p does the series p<3 n = 2 1 (n² In(n)) converge? (Enter your answer using…

A:

Q: Find all values of x for which the series converges. For these values of x, write the sum of the…

A:

Q: 1 (Kn)! संपो हे

A:

Q: (х — 10)" 00 10" n=1 WI

A:

Q: For what values of p is the series convergent? Answer (in interval notation): (Inn) Σ(-1) -1. n² n=2

A: Given ∑n=2∞(-1)n-1(ln n)pn2

Q: E[(0.8)" -(0.3)"] n=1

A:

Q: For which value of p the series n(1 + n converges. ps-2 p22 p2-2 p<2

A:

Q: For the given function, g(x), (a) Find a Power Series representation, (b) Write the first four terms…

A:

Q: Find the function represented by the following series and find the interval of convergence of the…

A: We are given the series,                                    . First, we will find the interval of…

Q: For what values of x does the series converge​ absolutely?  For what values of x does the series…

A: Notice that                   limn→∞n+1xn+1n+4nxnn+3=limn→∞1+1nxn+11+4nxn1+3n=limn→∞1+1nx1+4n11+3n=x

Q: Give an example of two series E an and Ebn, both convergent,such that anbn diverges.

A:

Q: Find all the values of a such that the given series would converge. (x - 7)"

A:

Q: If z and y are positive real numbers, which of the following conditions guarantees that the infinite…

A:

Q: 1 of the function f (x) = and put the series in

A:

Q: Find all values of x such that the following series converges:F (x) = 1 + 3x + x^2 + 27x^3 + x^4 +…

A: Here it is given that the series of…

Q: Determine whether the series k=1 3\k-1 converges and if so, find its sum.

A:

Q: For what value of x the infinite series A. w=1 n!x" converges?

A: The ratio test of convergence states that the series ∑n=0∞an converges if limn→∞an+1an&lt;1. In the…

Q: Find the sum of the series, if it converges. Otherwise, enter DNE. 8 Σ (-3)" w=1

A:

Q: Find all values of x for which the series converges. For these values of x, write the sum of the…

A: Let the equation be y, then  - y = ∑n=0∞5x-23nExpanding this series by putting n=0, 1, 2 ....y = 5 +…

Q: Find all the values of x such that the given series would converge. ∞ 7¹ (x-3)n n+ 3 n=1 Answer:

A: Solution in step 2

Q: For numbers 1 and 2, state whether each p-series converges or diverges (2 points each) 1 2. Zn=1 3n4…

A:

Q: The values of p for the series. Σ to be convergent #1lp-31 is p>4

A: Explanation of the solution is given below.....

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: Use the Root Test to decide whether 3 п the series EI is convergent or 8n+1) n = divergent.

A:

Q: (x – 9)" - 9" n=1

A:

Q: For which values of a the power series 00 n=1 converges absolutely and for which values of a it must…

A:

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: Given that the series En-1 an converges, determine if the series En-1 cos(an) converges or diverges.…

A: Using the necessary condition for the convergence of the series which is

Q: For each function, find the power series expansion and determine the radius and interval of…

A: The given function is fx=11+2x2.

Q: Find all values of x such that the following series converges. 00 5x n! n=1

A: Here given the seriesf(x)=5xn2n! We need to find out the radius of convergence using ratio…

Q: Apply the root test to prove that this series converges absolutely: (- 1)"*' 2" n=1

A: Ratio Testlimn→∞|an|n=LIf L&lt;1,then absolutely convergent.If L&gt;1 ,then Divergent.If L=1 then no…

Q: For each series, determine whether it converges absolutely, converges conditionally, or diverges.…

A:

Q: If E an is a convergent series with positive terms, is it true that the series ( a) Σ(1+ α) (b)…

A:

Q: Find the values of p for which the series converges. In n n= Answer (in interval notation):

A: Explanation of the answer is as follows

Q: Σ 00, (x- 3)" n=1°

A:

Q: Given the following series: (n + 1)x²n-1 3" n=0

A: Explanation of the answer is as follows

Q: For the given function, g(x), (a) Find a Power Series representation, (b) Write the first four terms…

A:

Q: For which values of x does the following series converge? Find the sum of the series when it…

A:

Q: For what values of r does the series (1-r)" n=0 converge ? For such values, express the sum in terms…

A: Solving by geometric series we have

Q: Find the sum of the series, if it converges. Otherwise, enter DNE. 6 Σ n(n + 2)

A: Given problem:-

Q: Find all the values of x such that the given series would converge. Σ (– 1)"(x")(n + 2) (11)" n=1

A: Here we use the ratio test for the convergence of the function:

Q: Give the interval on which the series converges. Write your answer in the form (x,y), no spaces. E…

A: Consider a power series ∑cnx-an. Then there exist a number R such that if x-a&lt;R then the power…

Q: x" Σ n=1 п+5

A:

Q: Find all the values of a such that the given series would converge.

A: