Show that n! > 3 for n ≥ 7

Q: If > Jak| converges, then 2 ak converges too. k=1 k=1

A:

Q: Find convergence radius of sequence  Σ (x^n/n(n+2))

A:

Q: Let (sn) be a sequence with lim sup sn = 10 and lim inf sn = 5. (a) Show that (sn) is bounded. (b)…

A: Consider a sequence, Sn, with lim sup Sn = 10 and lim inf Sn = 5. (a) To show that Sn is bounded. By…

Q: II. Prove if X and Y are the sequence of real number and converges to x a real number then product…

A: Given that X and Y are the sequence of real number And X and Y converges to x a  real number. The…

Q: D) { (-)"} [Select] [Select] converges to 2.

A: Please see the below picture for detailed solution.

Q: converge absolutely, non-absolutel

A:

Q: Could you plz prove "upper reimn sum is always greater or to lower reimen sum"thanks

A: This question is related to reimann integration.

Q: Prove that or quari -1+ X.- ズい 2. X. ntl converged number Ja to 2.

A:

Q: Q2:Expand using Maclourin series (1 - x 1-x² 2 ln(1 + x4) )? -

A: As per our guideline we are supposed to answer only one question of  multiple type of questions.…

Q: Evaluate the upper and lower sums for (x) Withh dlagr n = 2: upper sum lower sum Illustrate.

A: The given function is: fx=2+sinxThe interval is 0≤x≤π

Q: a) exists a, c ER such that for every n > 0. |an – al 0 of real numbers such that an → 0 and for…

A:

Q: Suppose we have a sequence of non-negative real numbers such that each element is strictly less than…

A:

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: the Sequence hver So Lalue. for

A: The given sequence is,

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 < k leaves. The degree of each leaf is 1. Let there be n vertices. There is…

Q: Prove that {x_n} converges. Need to use info in a) and b)

A: We have the following information from part(a) and part(b) for any a,b∈ℝ…

Q: Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i.…

A:

Q: 23: Test convergence for th 1- En-o)(x + 5)"

A: According to the guideline I am answering only first question. 1- ∑n=0∞ 34nx+5n   Ratio Test : A…

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: Use the limit comparison test to find the sum from k=1 to infinity of: [(5sin2k)/k!]

A:

Q: Poove 4 is an upper bound of f2,4) also poove sup (2,4)= 4

A: To prove that 4 is an upper bound of (2,4) and Sup (2,4)=4. Definition:1 Upper bound : Let S is a…

Q: e radius of convergence of 5 (n+6) (x+4)" is: (7) "n .1 3 .2 4 .3 .4 7 Oun

A: We will find the radius of convergence

Q: Use limit comparison test for sum of n=1 to ♾ of (3n^3+2)^(1/2)/(8n^2+9n+1)

A: take bn = 1/n  we know that if limn→∞anbn= finite  then by limit comparison test both series behave…

Q: Consider the infinite sequence of shaded right triangles in the accompanying diagram. Compute the…

A: First find the area of the biggest triangle whose height is 1 unit and base is also 1 unit, here…

Q: Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i.…

A: Since sn and tn is bounded then there exist some finite reals Us,Ls,Ut and Lt such that:  Ls≤sn≤Us…

Q: Find the maximum n such that the probability of getting no head in tossing a coin n times is greater…

A: When the coin is tossed, Chances of number of head is 1/2. When the coin is tossed 2 times, then…

Q: Use limit comparison test to determine convergence or divergence of    Sum from n=1 to ♾ of…

A:

Q: is it kue thak if Can) and Cbu) tuo sequences of real numbers such Hhat iaus bu for aull -nEN Iand…

A:

Q: Consider a sequence {X,,n = 1,2, 3, ·.} such that with probability Xn = 1 with probability a.s. Show…

A: @solution::::

Q: 9. Let {xn}, be a sequence of real numbers. What does the boundedness of this sequence mean?

A: Given xnn=1∞ is a real sequence.

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

A:

Q: 1 n In s n=2

A:

Q: Find the limit of the series (if exist) 1 -1 3/4 1/4 4/3 1/3 None WI

A:

Q: an conditionally converges then Jan] converges. n=1 n=1 True OFalse Rationale: Reset Selection

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

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

A:

Q: The series from n=1 to infinity of n(n+4)/sqrt(n^3+5n^2.  Does it converge or diverge?

A: Take n2  common from the denominator and then go ahead

Q: 1 Converges / Diverges Test Used: n(In n)3 n=2

A: Solve the series Using integral test

Q: 27 2 1-0°ス 2n り=o

A:

Q: The generating function of the sequence 5,5,5,5,5 is 1-x5 O (1-x) 5 1-5x° O (1-x) 1-125x5 (1-x)…

A: We need to find the generating function of the sequence 5,5,5,5,5.

Q: The radius of convergence of -2 (x+6)" is: n=1 (-5) " (n)

A: Radius of convergence is calculated as below, The correct answer is option 2 i.e., 5

Q: Use integral test to test for convergence or divergence of the sum from n=3 to ♾ 1/(n ln^7*n)

A: if integral is finite then series is convergent

Q: converges, because lim n! 2(n+1) n! = 0. (n + 1)! 2* n+00 True False Reset Selection

A: The given statement is true. Use the ratio test to find the evaluate the nth term.…

Q: Find interval of convergence  Summation from n =1 to infinity of ((n(x+4))^n)/3^n

A: Consider the given series as ∑n=1∞nx+4n3n. Here, an=n3n. Apply the ratio test to the series as…

Q: determine convergence by intergral test   sum from 2 to the infinity of 1/n（ln n）^5/4

A: We have given the series

Q: (-1)"(n² /n +3) (х-5)" 2" (n° +2) 3 n=1

A:

Q: Show that n* 3-" converges for all exponents k. n=1

A:

Q: The sequence {1, –2, 4, –8, 16, -32, 64, – 128,...} O a. converges to negative one. O b. converges…

A: Check the limit of nth term. If it exists finitely sequence is convergent otherwise divergent.

Q: Show that the real sequence ( 0,-1,2,-3 , .... , (-1)nn, .... ) where n is a value from the set of…

A: Consider the given sequence,

Q: portion

A:

Q: The sequence =n sin - converges Select one: True False

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.