Let r E No and n E N. In this problem, a general formula for o,(n) is found. (a) Let n e N. Prove that (ple+1)r – 1 o,(n) = II (2 p* – 1 pe||n

Q: Show that E=12n)/n! diverges. Recall from the Laws of Exponents that 2m) = (2")".

A:

Q: Prove that 1 Σ 2т log R + O(1) as R → 0 n² + m² 1<n²+m²<R²

A: To Prove - Prove that

Q: Let > 0 and 6 > 0 be real numbers that satisfy e' (1+a+²) = eª (1+b+ 2 ) eb Prove or disprove that a…

A: Its given that a&gt;0 and b&gt;0. We have to prove or disprove that eb1+a+a22=ea1+b+b22 is satisfied…

Q: Q3/ A: If A = 5i + 3j – k find /A/,/al

A: Lets find.

Q: tollowing Soint probability: 21 O 02 マ-1.す :-2 3) Nune 4) 8

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Q: 3. Prove or disprove the given statement. (a) If x e R, and x + 0, then 2x > x. (b) If n e Z*, then…

A: Given: (a) If x∈R, and x≠0,then 2x&gt;x (b) If n∈Z+, then 2n-1&gt;0

Q: 15. Find x so that m || n. (5x – 20)°

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Q: Question 5. Consider the following three statements about a real number x: • P(x): -1 ≤ x ≤ 3. •…

A: P(x) : -1≤x≤3 Q(x) : x2 &gt; x  x2 &gt; xx2 - x &gt; 0x(x-1) &gt; 0x &gt; 0 and x - 1 &gt;0 ⇒ x &gt;…

Q: Prove if equal to MPn (W) dx= 2" (n!)" (2n+)! that m is an integer

A:

Q: ·C) - G) + G)-G) + +-1 - Prove that for any positive integer n, 0.

A: Use simple property of combination.

Q: 2 Show that for n>o Ê i=0 (-1) ( ^^ ) = 0

A: We have to show

Q: 1 If z = 2 V3 -i, then find ()*

A: Given complex number is: z=-1-3i2 Find the conjugate of complex number: z¯=-1+3i2 Find z¯4?

Q: iid Let X1,, Xn N(u, o). Find 2(n 3) (X2+ + X(n-2)) + 16 X(n-1) +Xn if,E(i) 16 17(n-2) 16(n-3) 4…

A:

Q: 1 The Final value of F(s) =| 1 is s+3 O 3 O 1

A: Fs=1s-1s+3 Applying Inverse Laplace transform, we have L-1Fs=L-11s-L-11s+3⇒ft=1-e-3t   ( since…

Q: 42. Let e = 1+ 1/1! + 1/2! + 1/3! + Show that if k is a positive integer, then kle is not an…

A: Given , e=1+11!+12!+13!+....we need to prove if k is a positive integerthen k!e is not an integer

Q: If -5n-2, then f(3) is 04 O 55

A:

Q: 4. The generating function f(x) for the Fibonacci numbers 1, 1,2,3,5,8, 13,21, ... is given by OA.…

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Q: The table shows the scores of two students in Mathematics and English in 2-item seatwork. Englishty)…

A:

Q: What is the general solution for | a? (23 – 1)10 dæ? O 10(x³ – 1)° + C o 1 (2³ – 1)° + C 27 1 5 (a3…

A: An integral is given by, ∫x2x3-110dx. The objective is to solve the given integral and find its…

Q: Evaluate (23* e dx O (2e)" + C In2e O (Be)* In8e + C (2e)* In2e + C O (8e)* + C In8e

A:

Q: P2.1.6 Suppose A E R×n is symmetric and nonsingular and define à = A + a(uu" + vv") + B(uv" + vu…

A: The Sherman-Morrison-Woodbury formula is :- If (A + uvT) is invertible then :  (A + uvT)-1 = A-1 -…

Q: i. Given that log x=12, log, y = 15 and log, z = 18. Consider the following four logarithmic…

A: Given: logax=12, logay=15, logaz=18 To find the value of the logarithmic expressions and find how…

Q: Prove that T S. Prove that S £ T.

A:

Q: 3. For n e N, we define n! = (n)(n – 1)(n – 2)... (2)(1). E.g., 4! = (4)(3)(2)(1) = 24. Prove the…

A: Here we have to prove two statements.

Q: Evaluate 23x e* dx O (2e)x + C In2e (8e)* In8e + C (2 e)X In2e + C (8e)X + C In8e

A: Firstly, converting the product of the two terms into a single term.

Q: (8) Let p = 7. Compute the index of a with respect to the primitive root g = 5 for a 1, 2, 3, 4, 5,…

A: We recall the definition and solve this problem.

Q: /1- V1- V1- VI-….. then what is the value of x? If a = | O 0.816 O 0.618 O 0.681 O 0.716

A:

Q: Let A = {x e Z: 10|x} and let B={xeZ:15|x}. %3D Then * O Bc A O A=B O None of these O ACB

A: Suppose A and B are two sets . Note the following result : If x∈B for all x∈A then A⊆B . If A⊆B and…

Q: 1.5 Prove that |e=2=| 0.

A: We need to prove that |e-2z|&lt;1 if and only if Re(z)&gt;0 The solution is detailed below.

Q: The number e can be defined by e= (1/n!), where n!=n(n-1)-2-1 for n 0 and 0!= 1. Compute the…

A: For the solution of the problem follow the next steps.

Q: Which of the following expressions is equivalent to In(2z + 1)°e*-?)? Choose one answer O (r – 2)…

A: To solve the following problem

Q: 2 5 2 If A= 4 6. 4 then |A| is -1 2 -1. |A|=0 |A|=1 |A|=-1 O

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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.