Suppose that > ak = a and let c E R. Prove, in all the that (c-an) = gory detail necessary, = c•Q. k=1 k=1

Q: i. If n is positive integer, Find (√3+ i)” + (√3 − i)”. ii. Separate tanh-¹(x + iy) into real and…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Prove the following fact: A" = 3"-1A. 1 1 1 1 1 1 1 1 1 A =

A: Given, A =111111111  We have to  prove An = 3n-1A

Q: U is the set of the numbers on a 6-sided die and B is the set of numbers on a 6-sided die that are…

A: Given If U is the set of the numbers on a 6-sided die and B is the set of numbers on a 6-sided die…

Q: 8. The (2*+1 – 2k) = %3D k=0

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Q: B. Suppose that y1, Y2, ., YnidN (0, o2). We wish to find the most powerful test for Ho:02 = o3…

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Q: Let v = [1] and let z = [¹] x The Projx is equal to k k [21] where

A: Our objective is given below:

Q: Ex2:] If S:= {1/n - 1/m:n, mEN3, find inf Sand sup S.

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Q: 10) If 1+ abt = c where a, b, and c are positive, determine the value of t. %3D

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Q: Let flx)=x² and! gix)-Xr4. Find (gof)は) (fog)l-5)= (gof)(-5)= こくい(6。)

A: We have to find fog(x) ,gof(x)

Q: 2. (6 marks) Let a, b, c € Z with a 0. Prove that if a X (a + 2b + 3c), then a Xb or a Xc.

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Q: -dz < 2re?. z + 1 Jェ-1|=1

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Q: Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x:x>5}. Find a. D' b. D-A c. P(A)

A: Note:-Since you asked multiple subparts,according to our policy we can solve only first three sub…

Q: V2, V3 ¢ Q

A: We have to prove that K=E then prove that

Q: 6.) Derike the binomial idendity nent) (un-) C Hint: For mzz, c^)+2(^) +m?]

A: To derive the binomial identity22+42+62+.........+2n2=nn+14n-16

Q: If f'(t) = 9t² + e' and f(0) = 4. Compute f(3).

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: 2F. n 1 ;;1=2" (b), (26)

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Q: Let _X=R². Find M² if M= {(a,1)}.

A: Given that, Let X=R2 Find M⊥ if M=a,1.

Q: 13. Prove or disprove: Q/ZQ.

A: (.) We have to prove or disprove .

Q: et x + y+ z=5 where x, y, z E R. Prove that x² + y² + z² >

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Q: If xly, then show that ||x+ y|| = ||x- y|!.

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Q: B=(2,).Then 2 E3 %3D

A: Some definitions: Interval:  Let S⊂ℝ, then we say S is an interval if c,d∈S such that c≠d. Then, ∀…

Q: & 18) Vaing showj that the idently in

A: Using the identity 1+x2n=1+xn1+xn,                . . . (1) we want to show that 2nn=∑k=0nnk2.…

Q: (9) Let P, Q, R be (a) (¬P VQ) (b) (P mathematical statements. Negate the following statements.…

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Q: 2 If A = 22 and B = -70 6. 10 , verify that B = s-AS, where s = -19

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Q: n Show that (") = (,“,) n-r.

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Q: first prove that ()" <n! < ()" forn2 6.

A: We will prove                        n3n≤n!≤n3n for n≥6.

Q: 1.5 (+Jo.2262

A: Given expression is 1.51+30.2262.

Q: Prove that Σ(;) = 0.

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Q: • Find the two values oft such that 99% of the area under the t-distribution is centered around the…

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Q: 9.12 suppose; a 3. A. %3D bる 19. .bz .(3. olet (A) = 2.. assume that fhe de teminanf ef find this…

A: We have to find determinant

Q: 2.35. Prove that if x and y are distinct real numbers, then (x + 1)² = (y + 1)² if and only if x + y…

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Q: if N=xYフ。 Prove tha+ xx

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Q: I find B such that AB = C. If 5 0 3 A = 2 01 9. C = 3 5 c- (* :)

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Q: Find the value of n(A U B) if n(A) = 8, n(B) = 13 and n(An B)=4. n(AUB) = (Type a whole number.)

A: