Let xE [0,1] and n E N, show that the following inequality holds x2 x3 3 1+x + 2! 3! +.....+ n! (n + 1)!" Using this incquality, approximate the value of ve with an error value determined to be less than 10.

Q: Show the uniformly converge to F Fn CX) = X 12 Fn (X)= X 1X€ (-10] XER %3D

A: We know that if a sequence of function has bounded derivative the uniformly convergent

Q: For which of the sets below, does the property n > 53 for all x, E S ?imply that (x,) is convergent…

A: which of the following is correct ?

Q: * Show that the sequence (xn)n>1 in R, where In = 1- Vn' converges to 1.

A:

Q: find the value of p which the inegrad converges absauaysconditionally COSY

A:

Q: Suppose f(x) = N(h) + a,h + a,h² + azh³ + --. The value of N, (h) using Richardson's extrapolation…

A:

Q: What is the largest positive constant K such that if 0 <r < K, then (nl)2 must (2n)! n=1 converge?

A:

Q: Expand in ascending powers of x up to and including the term in x. 7x assuming x = 25 estimate v13…

A: Given: 1+x1-7x12

Q: if the Positive root aso: ax²+x-1=0 it is calculated using the recurring formula X₁+1 = 1 = a (x₁)²…

A:

Q: does not converge uniformly k! k=0 Prove that on R.

A:

Q: Find R and the Interval of Convergence o (-1)" (x)" 272

A: Given problem:-

Q: f(2) = an(z – 20)" n=0 radius of convergence 0 sup{r : D,(zo) CN}. ain in words what this…

A:

Q: (d) 5 (ar + 2)k 2k k=1

A:

Q: Use Meithemeıtical Incluctionn to prove that for ail W with nz 2 イナ·ナ 1 1t 2-3 1 t 3-4 0-1 1 2…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: (2k)!rk (3k)! (e) k=1

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The approximation of the root x' of the funetion f(x) = x* + x* – 2x² – 3x – 3 accurate to within…

A:

Q: Find the least upper bound and the greatest lower bound of S = { 2pg+1 PEN, q E N pq and prove that…

A: The given set is  S = {2pq+1pq, p∈ℕ, q∈ℕ}. Now, we know that for any p∈ℕ, q∈ℕ.    pq &lt; 2pq⇒pq…

Q: the valu e of P. for ubich for allna). fntegral Converges

A:

Q: . Find all values of x for which пх" n=1 (n + 1)(2x + 1)" converges absolutely.

A:

Q: If X1, Y1, are two positive unequal numbers and Xn = (xn– 1+ Yn – 1) and y,= Vx – 1 Yn –1 V n 2 2.…

A:

Q: 13.D. Show that, if we define fn on R by fa (x) 1+ n?x? then (fn) converges on R.

A: givenfn(x)=nx1+n2x2dividing numerator and denominator by x2fn(x)=nxx21+n2x2x2

Q: Find the interval of convergence for xn 5n 8 n=0

A: The given series,     ∑n=0∞xn5n

Q: The interval [0,5] is partitioned into nn equal subintervals, and a number xi is arbitrarily chosen…

A: The given interval is [0,5]. Find the xi.

Q: The sequence a, = sin (A) is unbounded (C) converges to a number less than 1 (E) diverges to…

A: Limit of a sequence

Q: Two finite sequences x[n] and h[n] have the following DFTS respectively: X[k] = {1; -2; 1; -2} and…

A: Given: X[k]={1:-2;1;-2}  H[k]={1;j;1;-j}

Q: For for any pestive integor n Show that %3DFHE nth fibonacci term fn=the

A: We need to show that , for any positive integer n ,  f1 f2 + f2 f3 + ....... + f2n-1 f2n = f2n2…

Q: Theorem 3. Every solution of Eq.(1) is bounded if a + < 1.

A: As per the information, we will first find a recurrence relationship of the sequence, then find its…

Q: Find the interval of convergence of E n(x – 8)" n=2

A:

Q: The interval [0, 4] is partitioned into n equal subintervals, and a number x, is arbitrarily chosen…

A:

Q: 4. (a) Suppose X ~ Uniform(0,2). Use the definitions to find E[X] and Var(X). ¬75 (b) Suppose X 1,…

A: Given two problem related to uniform distribution.  We have to find mean and variance in first…

Q: fle) sinzdz Compute

A:

Q: If (an) tends to infinity and (b,n) is bounded, with bn > 0 for all n, then (an/b,) tends to…

A:

Q: Consider ax with the given coefficients a,: (2x)" n = 1 ind the radius of convergence R.

A: In this question we will use basic of calculus i.e concept of infinite series. We will use ratio…

Q: (h) (3x)* (3.r)* 2k |1 k=1

A:

Q: Assume that f : [0,2] → [0, 2] such that f and f' are continuous. Morcover, assume that max |f'(x)|…

A: As per the question we are given a function f such that the maximum value of |f'(x)| is 0.517 And…

Q: If (am) is increasing and en (an) is bounded by M converges to a, {|a1\, |a|}. max

A: Let (an) is increasing sequence and converges to a,

Q: 1). If r is not equal to one, show that a + ar + ar^2+ ....+ ar^n= a( r^n+1 -1)/( r-1).2).…

A:

Q: determine the radius and convergence of E n=1 5xn/3n2

A:

Q: consider the following statement: if a sequence of measurable functions fn converges in measure to a…

A: It is given that "if a sequence of measurable functions fn converges in measure to a function f,…

Q: x" n n=0 n2

A:

Q: If f'(c) exists and f'(c) > 0, which of the following must be true?     a)f has no local extremum…

A:

Q: Given f: [2, )IR, prove that fn (x) = けx" It, converger uni formly to f6)-o.

A:

Q: Question attached.  I have found solutions to this probem on the internet, but I don't understand…

A: Let N be a given positive integer and let p be the least prime number greater than N + 1.Let n be an…

Q: Show that if f(x) is integrable on every interval of real numbers, and if a and b are real numbers…

A:

Q: Suppose f"(x) = N; (h) + a,h + azh² + azh" +-- The value of N, (h) using Richardson's extrapolation…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The Lucas numbers L; are defined as follows: (1) Lo = 2, L = 1; and %3D (2) L, = L,-1+ L-, for n E…

A:

Q: Suppose the interval [1,9] is divided into n subintervals of equal width, and Ck represents the left…

A:

Q: The set S on wc fn Cx) = 1+ x" Converges pointwire ?

A:

Q: Prove that the quantity S= -kΣP li(P) r=1 is a maximum when P, = 1/n for all r. Do this by showing…

A:

Q: Find the interval and the radius of convergence (- 1)"x" Σ n=0 3n+1

A:

Q: The interval of convergence of +o B(x+7)“ is

A: Given, ∑n=0∞8(x+7)n3n