Show by example that Σ(an/bn) may converge to something other than A/B even when A = gan, B = Σbn ≠ 0, and no bn equals 0.

Q: 9. Show that exp(iz) = exp(iz) if and only if z = nл (n = 0, ±1, 2, ...). (Compare

A: To prove that exp(iz)¯=exp(iz¯) if and only if z=nπn=0, ±1, ±2, . . ..

Q: Without doing any calculations in Aut(Z105), determine how manyelements of Aut(Z105) have order 6.

A: Given: Automorphism, AutZ105To find: Number of elements of AutZ105 having order 6.

Q: Suppose X~N(197,6), and Z~N(0,1). Then x = 189, is equivalent to z = ______

A: Given Information: X~N(197,6) So, mean μ=197 Standard deviation σ=6 X = 189.   Z-score or…

Q: CH 10.3 Class Expresse II Use the integral test 2° Σ 3+1 Convergent is to determine whether or…

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Q: 4. The function t:Z15 → Z15 is defined as t(r) = 3r – 5 (mod 15). (a) Find t({2,3, 5, 13}). (b) Find…

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Q: Show m*[(1+alpha/m)^m-1] is monotonic decreasing.

A: To show that the expression m*[(1+alpha/m)^m-1] is monotonic decreasing, we need to show that its…

Q: L[u(t – 3) (1²4' – 9 4')] = 81e-4s 2 (s-ln 3)3 8 (s-ln 3)2 64e-3s 2 (s-In 4)3 6. (s-In 4)2 81e-4s 2…

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Q: Write down the iterative map corresponding to the Newton's method solution of the equation In(x) 1/2…

A: Newton's method: It is an iterative technique used to find the approximation of the root of…

Q: Do c only

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Q: Q4. Either find the smallest positive integer solution to x² - 29y² = 1, or compute the 9-th…

A: We need to find the smallest positive integer solution to  or compute the  convergent to .We will…

Q: Give one example that: 1. Show that 1/2 (x - x^T) is skew symmetric. 2. Give one example that:Show…

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Q: 23) -4V192X 25) -4V216xy'z

A: Given query is to simplify the expression.

Q: is it seies converge ost not. 1-2)^

A: To find:

Q: Find sequences (xn) and (yn) so that xn - Yn 0 and yet does not converge to 1 Yn

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Let f(x) = cos(x²). Then f(20)(0) = Select one: a. Non of them b. 1 (10)! (20)! C. (20)! (10)!

A: Solve the following

Q: Consider the equation 3x² - e* = 0, which has a root in [0.5, 1.5]. Use the iteration *n+1 = et to…

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Q: Prove that if m is a positive interger, l'(-m+) = 1.3.5..(2m -1)

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Q: Suppose Y~ Binomial(n, p). Let pn = and define Pn-P În (1 – În) n R₁ = a. Show that R₂Z ~ N(0, 1).…

A: The objective of the question is to demonstrate that the given expression R1 follows a standard…

Q: (kx 3. -){(kx-ky +kz).

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Q: Prove that E (2s+l)=3n" whenever 'nisa psitre r'nisa pisitive intger. 32.

A: Given that,      ∑j=n2n-12j+1=3n2, n is a positive integer

Q: Let Sn=Vn. Find an and show that an O but that Sn=ER=1@k diverges. ->

A: Solution:-

Q: Find the positive root of [x e* = 2 ] by the method of false position (show only 5 iterations).

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Q: Compute the derivative of g(x) = | 1 dt. 2 1+t5 2" 1+æ15 1+25z 2" In 2 1+æ15 1+25z 2" 1+a15 1+25z 2"…

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Q: Consider the equation 2x - 1 = 2 on the interval [1, 2]. 1 +1 will converge to a 2pn-1 (a) Show that…

A: * SOLUTION :-   Based on the above information the calculation is given below.

Q: Prove for r ≠ 1 that ∑_(k=0)^(n-1)(rk)=(1-rn)/(1-r). If ∑_(k=0)^(n-1)(rk), then compute s(1−r) =…

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Q: Q3/A/ Prove that (") + („",) = (*). n+: \k+1. n %3| k+1

A: Given:

Q: Use the first three nonzero terms of the Taylor expansion for f(x) = In(1 + x) to estimate…

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Q: ¹).. Suppose that fn are integrable and ffn du <∞. Show that, if fn 1 f, then f is integrable and f…

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Q: Which formulas are tautologies? Select all that apply. (p-q)-(p¬q) O-(-piq) pvp O-(-p^ (pv q)) → q

A: The given formulas are p→q↔¬p∧¬q, ¬¬p∧q, p∨q and ¬¬p∧p∨q→q. To determine which formulas are…

Q: Let...

A: Given expansion formula is  a+bn=∑nkk=0nan-kbk

Q: 2 Construet a tnuth foble for FPv (avs )]^ [-RV(Qvs]] P>A1(eAR)]=> (R=>P)

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Q: Suppose X~N(125,16), and Z~N(0,1). Then x = 141, is equivalent to z = ______. (Round your answer to…

A: For large sample n&gt;30 so, it is a z test. x~N(125,16) =125+16 = 141= x.

Q: (e) Choose {X,}"-1 from [0, 1]. Let p, be the probability that X; + X;+1 < 1 for all i € {1,2, ., n…

A: Given thatXi for i = 1,2,3,...,n are distributed uniformly from 0,1. Let us consider two random…