Using the Error Approximation discussed in class, the smallest integer N for which 16 < .08 is n=N n2

Q: 31. n! it n n =D1 n = 1

A: The given power series,   ∑n=1∞n!nnxn

Q: Use the Ratio Test to find the radius of convergence of E (Use symbolic notation and fractions where…

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Q: What is the valoe of Gre your anwer as a fractuon

A: We use the sum of an infinite geometric series to answer the given question.

Q: For all a > 0 and b> 1, the inequalities In (n) ≤n, n < b are true for n sufficiently large (this…

A: The main objective is to write an inequality comparing (ln(n))8 and n. The expression ln n is…

Q: n E(-1)* k + k)"-1, n2 1. k=0

A: The given value of ∑k=0n-1knkkm=0. The main objective is to detemine the value of ∑k=0n-1knk2+kn-1.…

Q: Find a formula for the sum of n terms. Use the formula to find the limit as n→ o. 8 lim n3- 1)2 i =…

A: Let Sn=limn→∞∑i=1n8n3(i-1)2

Q: A Sequence is a number and rang is real whose domain is natural ..... function unbounded .b O series…

A: A sequence is a function whose domain is natural numbers and range is real.

Q: Show that for any k > 3, any tree with a vertex of degreek must have at least k leaves. The proof…

A: Suppose there are l &lt; k leaves. The degree of each leaf is 1. Let there be n vertices. There is…

Q: Prone the tollowing Stadement . Fa any integes thint comesder h as odd & also n as even) n22, n3 is…

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Q: Using Ordinary Generating Functions prove in how many ways the sum of 5 dices give n as a resul

A: The objective is to find the sum of 5 dices.

Q: Find a formula for the sum of n terms. Use the formula to find the limit as n → o. 5 n3(i - 1)2 i =…

A: According to formula:∑k = 1n k = n(n+1)2∑k = 1n k2 = n(n+1)(2n+1)6∑k = 1n k3 = n2 (n+1)24

Q: If Σan converges and an &gt; 0 for all n, can anything be said about Σ(1/an)? Give reasons for your…

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Q: Let 7(N) be the number of primes less than or equal to N (example: 7(100) = 25). The famous prime…

A: Consecutive integers mean the integers where each number is one more than the previous number. So,…

Q: A sequence {an} is called decreasing an S an+1 for all n E N. ulgn

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Q: An example of using the exclusion-inclusion formula is the following matching problem. An…

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Q: A Sequence is a whose domain is natural number and rang is real ........... unbounded .a O function…

A: Sequence: A sequence of real numbers is defined as a function f:N→R. Here N is the set of natural…

Q: Prove this identity between two infinite sums (with r ER and n! stands for factorial): (E) - (2.r)"…

A: Let the given series is ∑n=0∞ xnn!2   To prove: ∑n=0∞ xnn!2 = ∑n=0∞ (2x)nn!

Q: 1000n + 1 Determine convergence of Identify any tests you use by name. п4 — 9

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Q: 00 For which a does > n(In n)a converge? n=2

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Q: 1 diverges by comparing with n-. 16. Show that n² – 3 n=2 n=2

A: Given: The series ∑n=2∞1n2-3 To show: The given series converges by comparing with ∑n=2∞n-1.

Q: For all a > 0 and b> 1, the inequalities In (n) ≤n, n < b are true for n sufficiently large (this…

A: Please see the attachment

Q: n is bounded and monotonic for all n. n +1 6. Show that the sequence An

A: The objective is to solve the above question.

Q: Find the interval of convergence. (x + 4)" Σ (n In(n))? n=2 (Use symbolic notation and fractions…

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Q: Using Newton's forward interpolation formula, show that (n(n + 1) n3 2

A: Newton's forward interpolation formula is fa+hu=fa+u∆fa+uu-12!∆2fa+uu-1u-23!∆3fa+...            (1)…

Q: A sequence {an} is called increasing if an < an+1 for all n E N. ylgn ihi

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Q: How many perfect squares are there between 1 000 000 and 9 000 000?

A: Perfect squares between 1000000 and 9000000. Now, the square root of 1000000=1000 and 9000000=3000…

Q: 1064 التاريخ معنات 1105 نا بسبب 1085 The radius of Convergence is R- 4 H-W n Σbal) (2x-3)^2 (-1)…

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Q: A decimal approximation for √3 is 1.7320508. Use a calculator to find 21.7, 21.73, 21.732, 21.73205,…

A: Given:Given that a decimal approximation for 3=1.7320508.To find:we have to find the following 1)…

Q: 4- Table given below gives square root for integer. Using linear interpolation formula estimate the…

A: Formula Used: For two points x0, fx0 and x1, fx1 , if x0&lt;x&lt;x1 then  linear interpolation…

Q: Consider the sum. n4 k=1 Write a formula to compute the sum for any natural number n. Answer:…

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Q: Find a formula for the sum of n terms. Use the formula to find the limit as n o. lim n - 00 7 + in i…

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Q: Consider the sum. k3 n n4 k=1 Write a formula to compute the sum for any natural number n. Answer:…

A: Given sum, ∑k=1nk3n4

Q: Show that...

A: We have to show that: n1=nn-1 for n≥1. We know the formula, nr=Crn=n !r ! n-r ! Applying above…

Q: Find the least value of "n" so that, k=n 199 Sn 2k-1 200 k=1

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Q: аn +1 Suppose that An → 1 as n → o. Find the radius of convergence. 3n n=1

A: We will solve this problem in some steps

Q: (a) For all n N and a # 0, show that ak an k=1 (b) For a sequence (xn) in R, suppose that there…

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Q: Consider the real sequence {an} given by an = In n – In(n + 1), n e N. Justify whether (a) it is an…

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Q: The sequence {n³ + 1}~, is n=0 O a. neither increasing or decreasing for all n > 0 O b. both…

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Q: n which case do you need to use the Central Limit Theorem? When X is normal and n is any number When…

A: According to the central limit theorem, if the sample size is sufficiently large, i.e., the sample…

Q: HiW. Comparison lest tan n show whether (an) Converge n2 n=1 or divege

A: Given : The given series  is ;  ∑n=1∞an = tan-1nn2 To find :  We have to check whether the given…

Q: The first four terms of the sequence (Xn) are given by X1= 1, X2 = 5, X3 = 21, X4= 85. Therefore,…

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Q: Use the binomial approximation 1- x 1- x2 x3 5x4 7x5 for |x| < 1 to approximate the number. 2 8 16…

A: In the given question, we have to use the given binomial approximation to find out the value of √5.…

Q: Which of the followimg statements are correct for 22 ? n4 +1 n=0 I) converges by the nen term test.…

A: Given that, a_n = (n^2 + 1)/(n^4  +1) Let us consider, b_n = 1/(n^2) The infinite series whose nth…

Q: Genralize if the numbers 1 to n are placed around a circle in some order what is the best possible…

A: To find the best possible lower bound on k such that some set of three consecutive number sum where…

Q: A sequence {an} is called decreasing if An 2 an+1 for all n E N. صواب ihi

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Q: write down detailed e− N-proofs  i) (√n+7)/(n+5) converges.  ii) (n2−3i)/(2n3+2i) converges

A: Follow the steps.

Q: 5. At a local university, English instructors are supposed to grade essays in a class so thất the…

A: Given that n=22

Q: Find a formula for the sum of n terms. Use the formula to find the limit asn → o. lim 2 + n i = 1

A: It's a question based on conversion of limit into definite integral. Proceed as shown below...