8. (Chapter 10, #16) Prove that for every positive integer n, 2" +1< 3".

Q: 10. Show that the interval (0, 1) is covered by the open intervals In (1/n, 1- 1/n), n 2 3, but (0,…

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Q: 5. Show that Beta(a,b) belongs to the 2-parameter exponential family

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Q: 4. (a) Use Gauss's lemma to evaluate (), showing all working.

A: The given term is, 1119

Q: Compute etA for 3 3 4 A = 1 2 1 -1 -3 -2

A: Use the Taylor series of ex to solve the expression. Convert the equation into matrix equation and…

Q: Show by example that Σ(an/bn) may diverge even though Σan and Σbn converge and no bn equals 0.

A:

Q: Assume that after w months,butterfiles populace in 1000 is calculated as F(w)=12w+cos(16w)+n×100…

A: Minimum and maximum of a function depends upon all the variables present in the function.

Q: Prove that the sequence xn has a convergent subsequence. 3n4 sin n – 4n cos n2 + 2 a) Xn 5n4 – 8n –…

A: We have to prove that xn has a convergent subsequence in each of the given cases.

Q: Prove that 1 1 1 Lim Jan+1 + V2n²+n. /2n²+1 V2n²+2

A: Limit is defined as the value of the function , when number of terms tends to infinity.  It can be…

Q: 4. Prove Theorem 2.6.5.

A: Let p,q be any two distinct points on l. Let r be any point on l. Let m be the line containing p and…

Q: limx-4 (15-8x) = -17 %3D

A: By using definition of limit

Q: There is one male baby seal for every nine female baby seals. Let X be the number of male baby seals…

A: Let p=P(male baby seal) = 1/9 Here n=5 Note that X follows a Binomial distribution with n=5 and…

Q: 15. Let z = 2cos0 + i(1 – 2sin0) where -n < 0 < n Show that Iz – il = 2

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Q: 4. Use the binomial theorem to find the first th ree terms in ascending powers of x of (1

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Q: 1 1 +,++ 1 1 1 1 x = _ а а b and let and Dn On n-1 be, respectively, the last and Qn-1 last but one…

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Q: 4. Suppose we are in a parallel universe where 6 dollar coins and 11 dollar coins exist. Show that…

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Q: Prove Theorem 11.3

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Q: Proceed as in Example 3 in Section 6.1 to rewrite the głven expression using a single power serles…

A: Given ∑n=2∞nn−1cnxn−2+∑n=0∞cnxn+2 We have to rewrite the given expression using a single power…

Q: bute 80 identical pencils in a class consisting of 10 boys and 20 girls in such a way that each of…

A: Given:- Number of boys=10 Number of girls = 20 Number of Pencils=80

Q: Show that the sequence of functions on the domain [-1, 1] defined by if -1<r<0, 0, if 0 <x < 1/n, 1,…

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Q: Prove using the IVT. For all integers n, sinnx = cos x for some x ϵ [0, π].

A:

Q: 2. Prove that (1,1,1,...) converge to 1 in (R,).

A: Convergence of the sequence

Q: Give a recursive definition (with initial condition(s)) of (an) where (n = 1, 2, 3, . . . )

A: We have, an = 212nWe have to find a recursive definition with initial conditions of an starting from…

Q: 30. Let (zn) be a complex-valued sequence such that 1 Vn EN: (2n + 2zn). 3 Zn+1 Show that (2n) is…

A: Sequence of complex numbers is convergent if and only if both the sequences of real part and complex…

Q: converges, then C„-)" " con COr n=0

A: We have to choose the correct answer from the given option according to the given series

Q: prove its true by mathematical induction

A: The mathematical induction technique is used to prove the validity of the statement for every…

Q: We want to find the number of ways in which 3r balls can be selected from 2r red balls and 2r blue…

A: We have , 2r red balls and 2r blue balls . To find : the number of ways in which 3r balls can be…

Q: How many bitstrings are there of length 2n that contain exactly n “O"s and n “1"s? Prove your result

A: Given that,   The length of bitstring =2n, i.e If we have a bitstring, it should only contain 0's…

Q: Prove that In( +VI-X²³) = In ( ¹+ √1-x²) sech ¹(x) =

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Q: Find the recursion for a population that doubles in size every unit of time and that has 14…

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Q: 8. Show that the sequence f,(2) =. converges uniformaly in the region 1+ na l2l2 2, but does not…

A: Show that the sequence fnz=11+nz converge suniformly in the regionz≥2, but does not converges…

Q: Let X1, X2,... be a sequence of coin tosses and let Fn be the sigma-field generated by X1,X2,...Xn.…

A: From the given information, X1, X2, ....be a sequence of coin tosses and let Fn be the sigma-field…

Q: an 34an-1 – 289an-2 for n > 3 with initial conditions aj = 68, az = -1734. an

A:

Q: 21. Write the equation 1+3+6+10+…+ п(n+1) 2 п(п+1)(п+2) 6. using summation notation. Prove that the…

A: The equation 1+3+6+10+...+n(n+1)2=n(n+1)(n+2)6 is written as: ∑k=1nk(k+1)2=n(n+1)(n+2)6So the…

Q: {Xn} 3. Prove that the sequence 1+2n² 1-3n² Xn where is bounded.

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: Exercise 9: Prove by contradiction that 3 doesn't have a finite number of decimal places.

A:

Q: Show that there exists root in the interval [1, 2] of x = 2sin(x), and then use false position…

A: Intermediate value theorem:- If f is a function which is continuous at every point of interval a,b…

Q: (Xn) be a sequence of real numbers defined recursively by 1 = 1 and 1 7. Let X = In+1 =5(Tn +3) for…

A:

Q: Prove this Adams-Bashforth method using polynomial interpolation and prove it's second order…

A: As per the question  we have to derive the two-step Adams-Bashforth method by using polynomial…

Q: If ||<1, determine the maximum modulus f(=) =+1 (a) f(=)==-2z+3, (b) f(=)==+=-1, (c) f(=)= 2z-1' (d)…

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Q: 17. Prove thatsin x = =x 1-x2 dx

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Q: alue of the funo 3) in the i

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Q: 1.Find the interval and radius of conv. of In(1 - x2) ?

A: Maclurin series representation for ln(1- x2 ) is  ∑n=0∞-(x)2n +2n+1   (Why?) Explanation As ln(1+x)…

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: 5. Show that cos .3 G) do not converge.

A: We need to prove that: cosnπ3 does not converge This can be proved as follows:

Q: 7) Show that if a, > 0, and Lim na, +0, then the series aj + az + az + a4 + diverges.,

A:

Q: 4. Find the z transform of the sequence (2k} = {0,2,4,6,8, .} From ({k} (Izl > 1) (8-1)

A: In this question, concept of z-transform is applied. Z-Transform In its most basic form, the…

Q: 1. Find the first-order derives:

A: Given,      4x2+715x4+534x3-37x6+15x-30

Q: Let 0 < 0 < 1 be a rational number. Show that the sequence {cos(nT0)}-1 is divergent.

A:

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.