(a) X~N(62,81),P(55

Q: 2n2 +n+2 ii. Use the result in (i) to test for convergence = 1 5n3 + 3n

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Q: 1. Find the interval and radius of convergence for (x-2)" 1. Find the interval and radius of…

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Q: find the interval of convergence.

A: Apply ratio test and check weather series is convergent or divergent.

Q: The interval of convergence of Ln=0 +0o 2(x+7)" -105x-4 -10kxS-4

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Q: A sequence (ak) from k=1 to infinity has a corresponding sequence of partial sums (sn) from n=1 to…

A: Answer: ak= 1/(k(k+1))

Q: n-l (4x-1)*1 n=0

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Q: k2 Determine the interval and radius of convergence: > 034(*ー1)* k=0

A: To determine the interval and radius of convergy.

Q: k2 +1 Use the divergence test to determine whether ek +1 k=1 diverges or state that the test is…

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Q: Q. 8 Verify that f(x) = x' – 36x satisfies the hypotheses of Mean-Value Theorem on the interval |-6,…

A: The function is given as , fx=x3-36x verify the hypotheses of mean value theorem on the interval…

Q: 3. Assume the sequence of positive numbers (sn) increases monotonically to infinity. Prove that Sn+1…

A: Let Sn be a sequence of positive numbers sn increase monotonically to infinity. ⇒limn→∞sn=∞     ∵ sn…

Q: 1es of index numbers was constructed with the base 1988. By 1992.. rose by 20%, while the link…

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Q: xercise: ind the values of X,, X2 and X3 using Gauss- eidel and Gauss-Jacobi Method. Show pur table.…

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Q: limit as n approaches +infinity of (n/(e)^n)

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Q: 7. Find the radius and interval of convergence. (л — 2)" a) > (x + 1)" b) n 3n+1 nº 5n n=1 n=1

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Q: k 7) Determine the interval and radius of convergence for E k! x"

A: Given

Q: (x + 2)" Determine the interval of convergence of 3n +1 n=1

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Q: 8. 2) Find the interval of convergence for the powen (n+ 1): (x – 1 n=0

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Q: or a series of dependent trials the probablity of success on any traip is (k+1)/(k+2)

A: Given: for a series of dependent trials the probability of success on any traip is (k+1)/(k+2) Here,…

Q: Q 3 ) Find the interval of convergence: 00 n° (x + 5)" 6 n=1

A: We use Ratio Test to find interval of convergence

Q: (4n². En=1 2 - 2n + 6, - limit comparison test -1 (8,² + n – 8) 7

A: The given series,      ∑n=1∞4n2-2n+68n7+n-8

Q: 5η X b) Σπ n! n=0 8

A: Given series is ∑n=0∞x5nn!

Q: 1) Determine the interval and radius of convergence of (x-2)" (n+1)5*** 8. Σ n=0

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Q: 34 (x – 2)* – 2)* - Find the radius and interval of convergence of k2 k=1 8

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Q: determine the interval and radius of convergence 1 Z-3)2+"(n² + 1) (4x - 12)" n=0

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Q: 9. Find the radius of convergence and the interval of convergence – justify your answer. S-D*(x-6)*…

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Q: (-1)+ (x+2)" Example / Find the interval of convergence of E-

A: Here we have to find the Interval of convergence ,  ∑n=1∞(-1)n+1(x+2)n2n×n

Q: 2n+1 Test the convergence of E 2n=1 by limit comparison test. Vn3+1

A: we have to test the convergence by limit comprison test

Q: Σ Why can't the integral test be used for the series K! K= 0 The function is not decreasing for all…

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Q: (x + 2)" Find the interval of convergence for 22(-3)n n²(-3)" n=1

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Q: 1. Find the interval and radius of convergence 00 (4x – 2)" (-1)" (4n + 1) n=0

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Q: 4 interval of convergence. f(x) 2х+3

A: Given data:     The given function is: f(x)=4⁄(2x+3). STEP-1 The given function can be written as,…

Q: Σ (x – 3)" 2" +1* Determine the interval of convergence of n=1

A: Given:

Q: 2. (a) For n ≥ 0 and x E R, prove that (b) Prove n n Σ ^ (^.) 2^* (1 - 2)"-* k k=0 = = In. n x)n-k…

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Q: Show graphically of the inequality 1. 2x+3y+5>o

A: Inequality: Linear equality is expressed of the form ax+by+c≥≤0. Instead of equal sign, an…

Q: What the domain of convergence Fn(x)=X^n

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Q: Use initial value theorem and final value theorem to find f(0) and f(0), if 6+ 7s² + 5s F(s): s(s2 +…

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Q: There are 25 prime numbers less than 100. The Prime Number Theorem states that the number of primes…

A: Given, Px≈x/lnx     ......(1) (a) find P(1000) put x=1000 in equation 1…

Q: (-1)" Σ uzt Find the interval and radius of convergence for: k" n=0

A: Here, I have used D'Alembert principle to determine the radius of convergence.

Q: 3n? is increasing. Find an upper bound. n2 +2 Show that an

A: Consider the sequence and check whether Sequence is increasing or not.

Q: The interval of convergence of (-b)" x"*1 where b > 0; is n+1

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Q: f(x) = x^2 between x = 2 and x = 6 using a right sum with four rectangles of equal width.

A: Explanation and solutions is given below.....

Q: 2n2 +n+2 Σ ii. Use the result in (i) to test for convergence = 1 5n3 + 3n

A:

Q: 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points…

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Q: (-1)"3na" n -5 V. Determine the interval of convergence of

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Q: (x – 3)" 2n +1 - Determine the interval of convergence of n=1

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Q: ZNTI for |k| < N. Then, for Y let py (k) = 2-k, for k = 1,2, -.., and for Z let Define the following…

A: Given: pXk=12N+1 for k≤N……1pYk=2-k, for k=1, 2, ………2pZ-1=0.25……3pZ1=0.25……4pZ0=0.5……5   Also, except…

Q: k2 Use the integral test to determine whether 2 1319)2 converges. (k3 + 9)2 k=1

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Q: he radius of convergence 7n E(-1)" (3n)! n=0

A: We have; ∑n=0∞(-1)nx7n(3n)! where an=(-1)nx7n(3n)!

Q: 2n Use the Ratio Test to show that 3n has radius of convergence R = 3. .2n n=0

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Q: 5 (-3)" -(x + 3)". Vn n=1 Find the radius of convergence R. If it is infinite, type "infinity" or…

A: Consider the power series ∑n=0∞cn(x-a)n. Suppose that the limit limn→∞cn+1cn exists or is ∞. Then…