The expansion of eSin(x) is? Select one: - */a +... O a. 1 + x + *½ O b. 1 + x + */2 + * +. O c. 1 + x - *½ + * O d. 1 +x + */6 - *ho+... /½ +... ho +..

Q: Show that the middle term in the expansion of (1 + x)2¹ is (1-3.5 (2n- -1)) 2"x", where n is a…

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Q: Let f(x), g(x) be palynomials in 26 [x]. Find f(x) g(x). Write the polynomials as sequence (a, a,,…

A: Given: fx=4x3+2x2+x+3 gx=3x4+3x3+3x2+x+4 are polynomials in ℤ5x. To find: fxgx for the given…

Q: Q2/ Fin x in the

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Q: Suppose that {an} is defined recursively by: an = (an-1)² - 1 and that ao = 2. Find a2 and az.

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Q: Use induction to show that Vn EN, 6| 7n – 1.

A: For the solution follow the next step.

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: The following is a valid identity, true or false? P(k): 1+2+22 +23 + .. +2k = (2(k+1)/2) +…

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Q: 2. n³+3n²-4 = 0 (n³)

A: We have used definition

Q: Show that 1+2+3+… +n = (";").

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Q: (1+ 2x + 4x + 8x° + · · · )(3x + 3x* + 3x° + · · · )(x° + 2x° + 3x° + •..)

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Q: (1+ 2x + 4x? +8x + ...)(3x² + 3x* + 3a° + · . .)(x³ + 2a® + 3x° +

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Q: Let $n$ be a positive integer. Among C(2n,0),C(2n,1),..., C(2n,2n), C(2n,n) is the largest. True…

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Q: If the coefficient of 4 consecutive terms in the expansion of (1+x)" are a₁, a2, a3, a4…

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Q: ) 6. Express the sum 9 + 28 + 65 + ... + (n'+1) using E-notation.

A: We have to find sum of series:

Q: (A) = and (B) = . Find 2A - BO* none of the above

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Q: find the Maclaurin expansion of e-2x In(1+x)

A: fx=e-2xln1+x

Q: Use Pascal's Triangle to expand the binomial (x + 1)° O 25 + 5x4 + 10x + 10x2 + 5x + 1 O g5 - 5x1-…

A: Pascal's triangle…

Q: 3 O Find the first three terms of the expansion of (1+x)(2x-1)

A: The given series is 3(x+1)(2x-1) We have to find first three terms of the given series. This can be…

Q: Use Parseval's equality to show that 776 960 = n=1 1 (2n-1)6*

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Q: 1.5 Inx - In(x2 - 1) + 2ln(x + 3)

A: Logarithm simplification

Q: et Find the Maclaurin expansion of : 1+x3 O a. x² 5x 23x+ 1- x + + 6 24

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Q: 3. (a) If etB and eta are both contractions on R", and BA is a contraction. Similarly for…

A: We  have  first recall  the definition of contraction map.Let   be a  function.Then,   is  said  to…

Q: Show that 2n is O(3n) but not that 3n is not O(2n)

A: We need to show that 2n is O3n but 3n is not O2n Definition of Big O notation: Let f be a real…

Q: -1/2 p. Find the coefficient of x" in the expansion of (1– 4x)2.

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Q: 7 The coefficient of x³ in the expansion of | x+ 210 21 42 105

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Q: Find the general solution of the recursive relation an = 2 an-1 - 6 an-2 for every integer n > 1. a,…

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Q: Which of the following is not a possible variable term in the expansion of (x + y)6?  xy5  x4y2…

A: Given the query is to find which can not be the term in the expansion of (x+y)6.

Q: Find noots in trorms ob K (Itk) (8"+hdT h )

A: Given the function

Q: Find all the conjugacy classes of D4.

A: We have to find conjugacy Classes of the Dihedral Group, D4