17. The coefficient of x²y² in the expansion of (2x + 3y)4 is O 186 O 216 O 124 none of these

Q: Find the term independent of x in the expansion of (2+ x²)°|1 2 3 1-). x2

A: Given- 2+x261-3x22 To Find- The term which is independent of x. Identity Used- For a general term of…

Q: The first term in the Binomial expansion of (3x-y) is: None |(3x)y |(3x)6 |(3x)®y 1

A: general term of binomial exxpanson (a+b)n is Tr+1=nran-rbr

Q: 20. What is the value of the 4th term of the expansion of (y + 2z)°? 16y"z 448y 23 25628

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Q: In the expansion of (x+y)35

A: We use the Binomial Theorem to find the required coefficient in the given question.

Q: 20 Term independent of x in expansion of x2 5 + 6x3 is? e 7

A: Here we have to find the term independent of x.

Q: 16. The expansion of (2 + 3x;-1 is valid when >x>

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Q: Determine the coefficient of x3 in the binomial expansion of (1 + 5x)½ by completing the given…

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Q: What is the coefficient of the x^7y^4 in the expansion of (x+y)^11

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Q: D. Show that if a, = 3n³ - 17n² + 2n - 6, then an O(n³).

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

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Q: Suppose n E Z. Prove that if n is even, then n2 + 5n + 4 is even.

A: Note: We know that the square of an even number is always an even number, since  Let x is an even…

Q: 1. the largest term in the expansion of ( 1+x)^19 when x= 1/2 is ? 2. If the 2nd,3rd and 4th terms…

A: (a) As we know that from the binomial expansion, (r+1)th and rth term is given by…

Q: 5 Find the coefficient of x in the expansion of x- The coefficient of x is

A: The general term of expansion of (a+b)n  Tr+1=Crnan-rbr Here, a=x, b=-2x, n=14 So, Tr+1=Cr…

Q: 1. Complexity 2n – n³ + 2 Prove that O(n) 3n2 + 4n – 1

A: The big O notation is used to mention the important term r the biggest term in the equation. The…

Q: What is the value of Z if only 1.5​% of all possible Z values are​ larger?   The value of Z if…

A: From the provided information, The value of Z needs to be calculated if 1.5% of all possible Z…

Q: The order of the element 3 in Z24 is

A: Given: Z24 Formula Used: The order of an element k in Zn is given by Ok=nhcfk,n

Q: Prove that (n – 1) +n° + (n + 1)° is divisible by 9 for n E {1,2,3, . }

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Q: 1) Write all the following as expansions : > 0.2 > V26 V35 (0.99)-4 V(4 – 2y)2 ,y<2 2х-1° 2

A: (a) 0.2answer(a)0.2=2100.2=15(b) (26)13 answer(b) using approximation to solve the cube rootput x=27…

Q: The coefficient of xy13 in the expansion of (x + y)¹8 is O 43,758 O b 31,824 18,564 8,568 C Od

A: We know (r+1)-th term of binomial (x+y)n is  Tr+1=Crnxn-ryr

Q: Σ 9n n = 1 Identify an-

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Q: (-1)"(n + 2) 2n+1(n + 1) 4. Compute the exact value of n=0

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Q: Compute the coefficient of xy4 in the expansion of (3x – 4y)7. -

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: Prove that n3 + 2n is divisible by 3 for all n E N.

A: We prove that n3+2n is divisible by 3 for all natural numbers n.

Q: 4 Which of the following is the correct expansion of (3x - 3y)2? 9 x2 - 18 xy + 9 y2 9 x2 - 9 y2 9…

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Q: What is the coefficient of x'y5 in the expansion of (1x + 3y)18? 3,15

A: Use formula of binomial expansion to solve the question.

Q: (-1)"(n+ 2) 2n+1(n + 1) 4. Compute the exact value of n=0

A: Given series is  ∑n=0∞-1nn+22n+1n+1

Q: Find the specified n-th term in the expansion of the binomial. (x+y)10, n = 3 O 44 xy² O 47 xy2 O 46…

A: Let' s write the Nth term for the binomial expression , ( a + b ) N  Here a and b are real numbers…

Q: The first three terms in the expansion of (1 + ay)^n are 1, 12y, and 68y^2. Find a and n.

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Q: 2. Consider the expansion of ( 2x + =). Assuming k is a positive constant, suppose the term 8.…

A: Soln :- (2x+kx)8 ∴ The term independent of x is 1451520 ∴ (a+b)n =∑r=0ncr arbn-rn

Q: 12. The first four terms of the binomial expansion of (1 - )' A I+ 4x + 7x² + 7x B 1- 4x – 7x + 7x³…

A: 1

Q: paper 2 4. INDICES AND S 2007 N Q3 (i) Express 9x+1 as a power of 3. (ii) Express V272 as a power of…

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Q: 2n 2n 1/2n + 2 1, 2 n +1 n -

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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: Prove that n² +n is divisible by 2, where n E N.

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Q: prove by mathematical induction + E+ 7.16 +.. 1 1 (Зп-2)(3п+1) 3n+1

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Q: 2n Using the expansion of (1 + x)² and given that 2nC₁ + 2(²nC₂) + 3(2n C3) + ... + 2n(2nC₂n) +…

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Q: 1) Write all the following as expansions: > 0-2 > V26 > V35 > (0.99)-4 > V(4-2y)2 y 2х-1 A A

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

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Q: Show that 6n – 1 and 12n+1 are relatively prime for any n e Z.

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Q: 5. What is the coefficient of x''y" in the expansion (- 3x + 4y)ª . Show your work here:

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Q: 2. In the expansion of (2x + 3y)(4y – 3x) the xy term is : А. — ху В. + xy С. 8ху D. -9ху

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Q: QUESTION 3 Prove that 2n > n2 if n is an integer greater than 4. For the toolhar press AIT. E10 /RCL

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Q: Question 4 Use Mathematical Induction to show that 512|8 · 5" +6. 32n – 80n – 14 for all n E N.

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Q: 3. If the coefficients of 4 consecutive terms in the expansion of (1+ x)" are k1, k2, k3 and k4…

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Q: = 14 |1 + 0 (())| for all i with (b) n = 4 [1 + 0 ()“)- (a) qki (x1); + 0, 2k

A: a) Given that λ1&gt;λ2≥…λn Now,  x1Ty0 is not equal to 0 Now, expanding it  yo=a1x1+…anxn so that…

Q: 2 O Expand Pn = 2x +3x +) in Term of P.f,.

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Q: (4a) Let n E Z. Prove that if n is even, then -5n – 3 is odd.

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Q: Find the term of free x in the 10 2 expansion of (x² + 3)¹0.

A: