Show that when |+ 1|<1, = =1+E(n+1)(=+1)"

Q: Express f(=) = in a series of positive and (: – 1)(:– 3) negative powers of (: – 1) -

A: Given problem is :

Q: Find the interval of convergence of ∞∑n=0 (x−2)^n/n+ 3

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Q: limit as n approaches infinity of (1-n)/(3n+5)

A: Let's find.

Q: - Find the interval of convergent for : 2n 2 2n! n=0

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Q: What is the convergency interval of (-1)"-_(*-2)* 3-(2n+1) {(-)

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Q: 4. Find the interval of convergence E (2x+3)"

A: Here we have to find the interval of convergence ,  ∑n=0∞(2x+3)n

Q: If n = 18, then the interval of the form (- t(n-1), alpha/2 , t(n-1), alpha/2), that contains 99% of…

A: From the given information, number of observations n = 18. Confidence level  Level of significance

Q: The value (x, f(x)) of the maximum or minimum limit of the function 8 + f(x) = x3 - 6x2 + 4x and for…

A: Please see the attachment

Q: Find the interval of convergence. (x + 5)" Σ (n In(n))² n=2

A: To Find: Interval of convergence of given series…

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

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Q: Find the radius of convergence and the interval of convergence:2n-02)3-2n 61-n 2. (x+ 4)"

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Q: 4) Find the interval of convergence (x-2)" 8". n of n=1

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Q: (2n+1)! (x-2) n=0

A: We have to find the radius and interval of convergence.

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

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Q: 2n + 5 9n + 4 n=1

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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: (x-1)" 4n.5n n=1

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Q: 9. In(1 – x²) = -) on the interval (-1, 1) n=1

A: We know that ln(1-x)=-x-x22-x33-x44-...=-∑n=1∞xnn     ...(1) on the interval (-1, 1)

Q: Limit n---infinity for the function nln((1-(3/5n))/4 using L'Hopitals

A: Evaluate the given function  as follows.

Q: converges or diverge 2n+ Sin(n)

A: The given series is  ∑n=1∞    12n+sinn We have to check whether the series converges or diverges.

Q: The first derivative of the power series 9 9x2 9x3 9x4 f(x)=9+ .. is 1! 2! 3! 4! O -9 f(x) O f(x)…

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Q: Suppose a person invested 1 million dollars in a certain project in the beginning of year 2000. The…

A: Time and Confidence Interval                  Time interval is used in statistics to…

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

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Q: Suppose a increases on

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Q: The function ƒ(x)=x' – 2x - 4 has a root at x = 2, write one re-arrangement of the form x1 = g(x„)…

A: The given function is,f(x)=x3-2x-4

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

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Q: Find the interval of convergence of 2' > n(n + 1)(x – 2)" n=0

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Q: 2. Rainwater accumulates in the ditch as follows: 10 centimeters of water in the 1st second, 15…

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Q: find the interval of convergence.

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Q: determine the interval and radius of convergence. 61-n 1. (x+ 4)" (-2)³-2; n=0

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Q: 2x is an increasing function for x>0. 2+x Show that y = In (1+x)-

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Q: explain using a graph of (x) = X³-6x, for 0≤x≤3 With Six sub intervals, what the Riemann sum…

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Q: Find the interval of convergence for 3x+1 Σn(n+1)*

A: Given series is ∑n=1∞3nxn+1n(n+1)

Q: Use max-min inequality to estimate : 1 -x2 e

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Q: Find the radius of convergence for ∞∑n=1 (sin^2 (n))x^n

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Q: Find lower bound for f(n) = 5n².

A: To find the lower bound for f(n) = 5n2

Q: Find the derivative of the given power series x10 10 ,15 1 20 5 15 +. 20 .. + x° – x14 + x°+ x* +…

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Q: If sequence a_n of positive numbers in increasing, then it is not bounded. TRUE or FALSE

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Q: Find the radius of convergence for: 3 (n!) ³ (3n)! n=1 xn

A: Recall that the radius of convergence for a series ∑n=1∞anxn is R=limn→∞anan+1

Q: 27 2 1-0°ス 2n り=o

A:

Q: 41. Can √5 be approximated through fixed-point iteration? Define a f(x) and a g(x) to do this if it…

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Q: 8) FIND THE INTERVAL OF CONVERGENCE FOR Σ (-1)" x 1=2 n2^ n

A: The given series: ∑n=2∞-1nxnn2nWe need to find the interval of convergence.

Q: A colony of bacteria is grown under ideal conditions in a laboratory so that the population…

A: Given:At the end of 3 hours there are 10,000 bacteria.At the end of 5 hours there are 40,000…

Q: If In x + In(x - 7) = ln(7x), then x =

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Q: 2. Determine the positive real root of the function f(x) = In(x²) – 2 with initial guess [5/2, 3]…

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Q: 1 Show that the series 2 converges. k=2 k(log k)?

A: Given: ∑k=2∞1klogk2

Q: Prove that a sequence of positive real numbers {r„}1 tends to 0 if and only if the sequence {},…

A: We have to prove a sequence of positive real numbers xnn=1∞ tends to 0 ⇔ 1xnn=1∞ tends to ∞.

Q: Define the sequence of functions {fn(x)} on [0, 1] by { 2n2x; 2n(1 — пх); т. fn(x) : 0; n Find f(x)…

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Q: Present a combinatorial argument to justify your answer. How many increasing (not strictly)…

A: We have to find find total number of increasing functions from {1,2,3,...,n} to {0,1}. As a function…

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.