The small positive integer n for which (1+i)?n=(1-i)²n 8. O 12 2 4

Q: (a) Suppose that n > 1 is an integer with prime factorization n = pf"p.p. Prove that (k, + 1)(k, +…

A: As both of them are different questions(not a subpart of other), so as per the guideline, I am…

Q: The value of the triple integral 7/4 None of these O 7/12 O 7/3

A: According to Bartleby guidelines , we are supposed to do only one question. If you want more…

Q: For any positive integer n, n(n+1)(2n+ 1) EP = 12 +22 + .. + r?

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Q: 9. Prove the formula n(n+1) >i =1+2+...+n= 2 i=1

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Q: n be a positive natural nun (an)" is equivalent to: 4n Let a) n²n (n²-4n) b) n(n²^_^) d) na^ (^^-2^)…

A: Given, n4n-(2n)2n

Q: n(n+1)(2n+1) Prove: 12 + 22 + 3² + ... +n? for all positive integers, n.

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Q: O and Let the numbers c1, C2, . .. be defined inductively as follows: c1 for every n > 1 the number…

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Q: the statement below true or false for n=1? ©George Mason University 2+ 4 + 6+ ... + 2n = n² + n + 1

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Q: (-i)a is e(1+4n)i wheren is an integer. where n is an integer. O equal to the above O equal to the…

A: Any complex number, z can be written in the form of  z=reiθ . The complex number i can be written as…

Q: 1. Find the indicted term: an = (3n+ 2)²; a6

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Q: M -2 Find formulas for the entries of M", where n is a positive integer. M" =

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Q: 100 П 4n 2n n=1 k=0 k in front of the individual rk terms for all kEI

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Q: 40. Ifn is any positive integer, then (n- 1)(n-2Xn - 3) ... (3(2X1) = A e B. (n-1y C. n! D. (n-1

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Q: The sum of the first n positive odd integers = Check all the correct answer/s. Σ I T Σ(2x + 1) 2=1…

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Q: 2 Look at the following picture. 000 000 1st term 2nd term 3rd term Prove that the number of…

A: Given:

Q: 1 fn is a positive integer, then (D -a) II

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Q: Which of the following statement is always true? (a) p(2n) = p(n) (b) p(n) is always even. (c) Edin…

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Q: While proving- a(a+1)(2a+1) . is an integer for the case a = 6q +2 which of the 6 %3D following will…

A: Option (c) is correct. See the attachment

Q: 8. Vn E Z, if n is prime, then 2" +1 is also a prime number. 9. For every positive integer n, n2 – 2…

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Q: Select all expressions that are equivalent to (2n +6)(n+ 3). O a 2(n? + 6n + 9) 2n+ 6n +18 Oc 2n…

A: Given,  => (2n + 6) (n + 3)  Taking '2' common from expression , => 2 (n +3) (n + 3)

Q: 2. T = {m EZ| m 1+ (-1)^i, for some integer i} *

A: Given T=m∈ℤ|m=1+-1i for some integer i

Q: 1. If n is an integer, then 2n +1 is odd. 2. The square of any integer can be written in the form 3k…

A: 1) Given:     If n is an integer, then 2n+1 is odd.   Let n=1  then 2n=21              =2

Q: Consider a positive integer 1 < i < 9. Then, given T(n) = 2T([n / 2] + i) + n, show that T(n) E O(n…

A: Given: T(n)=2Tn2+i+n The positive integer 1≤i≤9

Q: 23 - where a and b are positive integers; How many b values are there for the condition 2a + 3b =…

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Q: (-1)"(п + 2) 2n+1(n +1) Compute the exact value of n=0

A: The geometric series formula is ∑n=0∞rn=11-r, where r&lt;1. Simplify the numerator of the given…

Q: 2. Let, a1= 3 and for n ≥ 2, an = 2an-1 + 1, express an in terms of n. for n ≥ 3, an = 2an-1+ bn-1…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS. WE ARE ANSWERING ONLY FIRST QUESTIONS FOR YOU AS…

Q: -10 -4 3 6 Qs: A- Given A = L -4 and B = -8. 2 -14 -28 Prove that: - AB+BA = -7 14

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Q: 00 Assume that S = (-1)"-1 and SN 1 (n + 1)5 (n+ 1)5 n=D1 T-1 Find the smallest integer N such that…

A: According to Alternating series remainder theorem, the error when series in computed upto n terms is…

Q: If a_1=9a1​=9 and a_n=4a_{n-1}an​=4an−1​ then find the value of a_5a5

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Q: 2 Let M 2 8 Find formulas for the entries of M", where n is a positive integer. 1001 100 J M" = 27

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Q: (-1)"(n + 2) 2n+1(n + 1) Compute the exact value of n=0

A: The ratio test can be used to assess if a series is converging or diverging. The following are the…

Q: 8. Let K be an integer that is greater than 1, a perfect square, and equal to Ei for some integer D.…

A: A perfect square is a positive integer whose square root is a positive integer. Example of perfect…

Q: 30. Find an explicit formula for a1=17, a,= a,-1+ 4, n 2 2. a. an= 4n + 13 b. a,=n +4 c. a, = 4n +…

A: Here given Thus

Q: 10) Which of the following shows the solution for n2 + 2n 2 24? A) 4十 -6-5-4-3-2-10 123456

A: The given inequality is n2+2n≥24

Q: which ones n 3n +2 have the Σ 2n + 3 n=2 same character ? n-1 4 3 n° +2 III. > 3 n° +3 1. E: II. E…

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Q: a) Prove that ε n(n+ 1)(2n + 1) Σ 6 i=0

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Q: [-3 Find all values of λ for which | Al3 - A| = 0, where A = 0 1-2 -1 -31 3 0 -1 -2]

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Q: 14. It is known that the positive integer n is so that 9" = 20589113m094649 The correct value of m…

A: here we make find the n value  here we can try and find that n =15 92 =81 93 =729 .......... like…

Q: 1. Prove that the sum of the consecutive cubes is given by this formula: n²(n+1) 4 13 + 23 + 33 +..+…

A: Given; 1) 13+23+33+...+n3=n2(n+1)2/4 Repost the next questions.

Q: (1 – iy3)i is | а. е where n is an integer. b. e(1+4n)n where n is an integer. c. e(1+2n)ë where n…

A: We are given : (1-i3)2i Let z=(1-i3) r=12+(-3)2=2tan θ=-31=-3 θ=nπ-π3 Now,…

Q: Show that the n-th tetrahedral number O_n is given by S_n= n(2n^2+1)/3

A: A tetrahedral number corresponds to a 3-Dfigure in the shape ofa tetrahedron made of spherical…

Q: Find an explicit formula for a = 17, a, = an-1+4, n22. a. a, = 4n + 13 b. a, =n +4 c. a, = 4n + 17…

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Q: If a_1=5a1​=5 and a_n=a_{n-1}-4an​=an−1​−4 then find the value of a_6a6

A: Given: a1=5an=an-1-4

Q: 10 m 1º tam ² (²+3/-1) = 0 () If Stan cot 9r² + 3r − 1 n r=1 where m and n are co-prime, find the…

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Q: ir is 1 None of these e(1+2n)i where n is an integer. equal to the above where n is an integer.…

A: Any complex number, z can be written in the form of  z=reiθ . The complex number i can be written as…

Q: Use Gauss’s trick to determine H(n) = 1 + 5 + 9 + 13 + … + (4n – 7) + (4n – 3) + (4n + 1) I'm…

A: Explained below

Q: (-i)ñ is e(1+2n)i where n is an integer. equal to the above O None of these +4n where n is an…

A: To solve this question we shall use the following identity      Identity:                   eiθ=cos…

Q: Given that 3 1 1 2 ]=[3 3 1 -3 2 %3D 1 2 -3 [ 3 -3 find an explicit formula for 2 -4 for any…

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Q: 2. The square of any integer can be written in the form 3k or 3k + 1, for some k E Z.

A: True. We use the fact any integer is of the form 3q,3q+1,3q+2.