п(п- 1) (п + 1) n Prove that i² – i = | 3 i=0

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: VnEN+, 5" + 3n > 22n+1

A: Given that the statement ∀n∈ℕ+ , 5n+3n≥22n+1. The objective is to prove the given statement.…

Q: Which of the following would be a valid post-condition of the following Hoare triple? x = = (i+1)!.…

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Q: prove if P>-l then Citp = I+np %3D n€ IN

A: The given statement is not TRUE. Counter example is taking n = 2.

Q: If n is an odd natural number prove that I =, xsinnx dx = sinx 2.

A: Consider the given: It is given that n is an odd natural number, Take n = 1,Substituting n=1 and…

Q: 6. Show that, for integer s, S. s! | x25+lexp(-ax²)dx =: 2a +1

A: Note: Given proof statement has a little mistake, I have proof the actual result. First i have…

Q: 8. The (2*+1 – 2k) = %3D k=0

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Q: Find (124 *1 L3) /(9+j 7)

A: This is a problem of complex analysis.

Q: Let M = MT= -3 12 -6 15 Find formulas for the entries of M", where n is a positive integer.

A: we have the matrix M=-312-615 now we have to find the formulas for the entries of Mn where n is a…

Q: TRUE OR FALSE  x and y are POSITIVE integers.

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Q: -4 M" = -127 14 Let M = 6 Find formulas for the entries of M", where n is a positive integer.

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Q: 3/2 (1 +i)"

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: Ź uk=2='In, find u00 u 100 Suppese that

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Q: if |z² + 1| = 2| z+1|  z e C then | z|  <= sqrt*7 Prove.

A: Given  z2+1=2z+1 , z∈ℂ            (i) Now,   z2+1=2z+1z2+12=4z+12 ,…

Q: 1 О. 15 Show that %3D (D - Q) k e k

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Q: 4. Prove that 3i² + i = n(n+ 1)?

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Q: 2 Find (5a" + 4a*) da 1

A: We can find the integration value as below

Q: 7

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Q: Let n 2 2. Assume that Fn is prime. show that -1.

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Q: (15 – b) (9 – b) - z = 6. 6. För a = 1 och b + 3 saknar systemet lösningar. För a = 1 eller (4t) , y…

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Q: The formula for slope between two points (x1, y1) and (x2, y2) is: m = 5-4 O True O False

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Q: T0 0 1 0 0 0. 1 0 0. Find A[9. 0 0 Let A 1 00 0. 0. 1 0 0. 0.

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Q: Show that 2"=nCk and 0 = [(-1)^nck k=0 HINT: Consider(1-1)" and (1+1)" k=0

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Q: 3. Compute |(1+ i)(1 – i)(1 + 3i)| .

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Q: *prove that for . P+2+3+... +n° = 2 n=!,2,3,

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Q: Prove that 1¹x 2² x 3³ x...xn" < n(n+1) 2 (2n+1) 3

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Q: Evaluate L{3(sin² 2t )} 24 24 24s 24 а) s(s² + 4) b) d) s(s² + 16) s(s² + 16) s(s² – 16) a O Option…

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Q: 44. (a) Let a, b, ceZ with (a, b) = 1 and a | bc. Prove that a c. (b) Provide a counterexample to…

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Q: Prove the follawing identities. 4-V. 4- V = AV (a) (b) M8 = A/1+ 4) (1+ A)" 2. (C) 4/f = I for Afn-…

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Q: Indicate the least integer n such that f(x) = (3æ³ + 2x²)(5æ5 + 4æ*) € O(x").

A: Finding f(x) explicitly using multiplication of polynomial. The highest power of x or degree of f…

Q: If m is a positive integer and x > 1, then show that 1-4¹ (-1)" xm+1 m! 2 F₁ m+1 m+2 2 2 dxm

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Q: enoitetimil torte stigasb = 4", where m, neN. 10. Prove the identity: 3 r=0 itong s

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Q: M = 4 3 7 Find formulas for the entries of M", where n is a positive integer.

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Q: Prove that Σ₁ iª = n(n+1)(2n +1) (3n² + 3n − 1) i=1 30

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Q: Prove that x" dx „n+1 + C, n + 1 for n + -1.

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