For every integer n23 I+ 2+ 2?+ +4^= 4(4n-16) %3D 3. Proof (by induction)

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A: Types of integers : Odd integers : The integer which is not divided by 2 . It has the form 2k+1…

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A: We have to evaluate the integral ∫ 6-4zz2z+3dz using the residue theorem. For this, we have to find…

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A: Consider the given expression. y3-12c29 The binomial formula is defined as,  a+bn=∑k=0nnkan-kbk As,…

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A:

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A: using formula:-

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A: when four positive integers are added three at a time the sums are 1551, 1659 ,1720 and 1736. we…

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Q: V nEN, 7"- 3n is a multiple of 4.

A: We have to find   For all n= natural number we have to

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A:

Q: Find the sum of the first 21 positive integers. The sum of the first 21 positive integers is

A: We will use the concepts of A.P.

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A: Let ab5c be all four digit multiples number 36 with different digits.   As 36= 4x9, so the number…

Q: Give a combinatorial interpretation of the coefficientof x4 in the expansion (1 + x + x2 + x3 +⋯)3.…

A:

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: We have given expression 3x2-y310 Then, fourth term of the expression…

Q: The sum of any two integers of the from 4k + 1is always: prime Zero Od Even

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Q: How do I find f prime of 3 if f(x)=13x/4+x2

A: Given,           fx=13x4+x2

Q: Every even integer greater than 2 is sum of two primes? Give your views on this?

A: We know that 2 is even prime. And all other primes are odd.

Q: Find all the odd positive integers n which satisfy ó(n) = 20. %3D

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Q: Suppose n is an integer and consider the number n* – 6n³ – 18n² + 6n + 1. a) By expanding the…

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Q: How many integers 2 ≤ n ≤ 65 have no prime divisor less than or equal to ¹/³?

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Q: How did they got n(n+1)(2n+1) / 6

A:

Q: What is the coefficient of x^4 in the expansion of (-1+ x)^11

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Q: z = -2 verify that |7 - 2| < |||| - |||

A: Given that y¯=−310 and z¯=1−21. We have to verify y¯⋅z¯≤y¯⋅z¯. Now y¯⋅z¯=−310⋅1−21=−5 Hence, y¯⋅z¯=5…

Q: :The nth term formula for { 1,0,1,0,... } is

A: given sequence 1, 0, 1, 0, .........

Q: Number of solutions of the equation 3x - 2x + 5x2 + x+2= 0 under modulo 5 is'are OB. OD 3

A: Consider the given equation, 3x4 - 2x3 + 5x2 + x + 2 = 0 The set modelo 5 is, ℤ5={0, 1, 2, 3, 4}…

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Q: Prove: “The sum of two even integers is even.”

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Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: The expansion of an general expression is given by (a+b)n=∑nkan-kbkk=0n  so any term can be found…

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Q: an 34an-1 – 289an-2 for n > 3 with initial conditions aj = 68, az = -1734. an

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Q: how many positive integers n satisfy 22-5n>-3?

A: 22-5n&gt;-3

Q: Solve for n: 6(п — 4) 3 а(n + 3) - Preview = U

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Q: Which term of the expansion of (x + 7)° contains x° Term number contains x°.

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Q: Use binomial theorum to expand (1 + 1/x)^7

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Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: Given To evaluate

Q: How do I find f prime of 13x/4+x2

A:

Q: how did they get 9x^2 from (x^4)/(5x^2)mod11 ?

A: Use of z11[x],

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: Given expression: 3c+c247 Concept used for the general term:…

Q: Prove that the difference of squares of any two odd numbers is múltiple of 8. (SOlve this task…

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