Which term will be a constant term in the binomial expansion of | x- إختر أحد الخيارات none of these o 2nd co 3rd do PREVIOUS ACTI

Q: TION 9 Prove by Induction that for every natural number n, 3"–1 is a multiple of 2? Attach File…

A: We prove by induction

Q: Find the length of the func tion based Vange de fincd belouw: the on 10<x <29 10

A: We have to find the length of the given function in the range 10 ≤ x ≤ 29. y = 110ex+e-9x

Q: Use Theorem 9.17 to give an upper bound to the 40th truncation error for the series (-1)" n2 n=1…

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Q: u will prove that 7*+1 - 1 is divisible by 6. ypothesis, since 6 evenly divides , there exists an…

A: We will fill in the blanks.

Q: An theorem that specifies the complete expansion of a binomial raised to any positive integer power…

A: Complete expansion can be done by theorem

Q: Establish by mathematical induction that any postage of at least 12c can be obtained using 3c and 7c…

A: We have to establish by mathematical induction that any postage of at least 12c can be obtainedusing…

Q: Use Fermat's little theorem to find the least residue of 8^70 modulo 23

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Use the power series expansion of ƒ(x) = 1 x)²· 1- x for x < 1 to find a power series ex

A: Remember power series expansion for f(x)=11-x; x&lt;1 is  f(x)=11-x=∑k=0∞xk

Q: 4. Find the first three nonzero terms in the Mac expansions of cos(x)/(1+x) by any algebraic method…

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Q: Find a Power Series Representation for 3-x2 Show all of your woi

A: We have to find the power series

Q: What is the smallest integer that is a quadratic residue for all prime moduli p > 2?

A: We know if there is an integer 0&lt;x&lt;p, where p is a prime, such that x2≡qmod p, then q is said…

Q: Find the term with no x in the expansion of x 15

A: we have to find the term with no x in the expansion of x3+12x-215.  as we know that the (r+1)th term…

Q: Suppose that you have 3 and 8 cent stamps, how much postage can you create using these stamps? Prove…

A: We shall show that every postage &gt;=14 can be created using 3 and 8 cent stamps. And then deduce…

Q: Q2:Expand using Maclourin series (1 - x 1-x² 2 ln(1 + x4) )? -

A: As per our guideline we are supposed to answer only one question of  multiple type of questions.…

Q: Expand sec(x) by Maclaurin series.

A: Maclaurin's series of any function f(x) is given as,…

Q: Find a recurrence relation (with initial conditions) for the number of n-digit (n greater or equal…

A: Given:     The number of n digit ternary sequence without an occurrence of the substring 012.  A…

Q: Use the binomial series to expand the function as a power series. 3 (4 + x)3

A: Given that              3/(4+x)3 Here we expand the function as a power series by using the binomial…

Q: Use the Master theorem to give an asymptotically tight solution to the recurrence below. If it does…

A:

Q: Prove that the summation of three odd integers is odd.

A:

Q: Use the binomial series to expand the function as a power series. 9. (6 + x)3 n = 0

A: Given: 9(6+x)3

Q: Find manually the first three nonzero terms of the Maclaurin series expansion for f(x) 3x+1 using…

A: Given: The given function is f(x)=3x+14

Q: Write the expansion of each expression using sigma notation. 19 (-Sm – 7n)" 19 19-7 (-Sm)"(-7n) Y-0…

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Q: 2. Suppose that the number of bacteria in a colony triple every hour. a) Set up a recurrence…

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Q: Find the sum of the positive even integers up to and including 50.

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Q: Ahmet borrows n TL from Burak. Starting from today, Ahmet pays back to Burak 2 TL or 3 TL at each…

A: Given that Ahmet borrows n TL from Burak. Starting from today, Ahmet pays back to Burak 2 TL or 3 TL…

Q: Show that there are infinitely many primes of the form 6k + 5.

A:

Q: Describe an algorithm that takes as input a list of n inte- gers in nondecreasing order and produces…

A: Fact :-  a list of integers is nondecreasing if each integer in the list is at least as large as…

Q: Use generating functions to find the number of ways toselect 14 balls from a jar containing 100 red…

A:

Q: Write out the first six terms of the sequence defined by the recurrence relation with the given…

A:

Q: Use the binomial series to expand the function as a power series. 9. (6 + x)3 Σ n = 0

A: As per guidelines we can solve

Q: Solve these recurrence relation together with the initial conditions given an=-6an-1-9an-2, for…

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Q: ar – 5ak-1+ 6ak-2 = 5k, ao = 1, az = 3

A:

Q: Use Pascal's triangle to expand each binomial. (x – 5y)s O us - 5ytx + 25y³r² – 125y²x³+ 625yx* –…

A:

Q: Write out the first six terms of the sequence defined by the recurrence relation with the given…

A: Given:                         x0=1;xn=2xn-1; for n≥1   To determine:                        First…

Q: 2. Find the largest negative x € Z that simultancously satisfies 4x = 9 (mod 5) 2x = 0 (mod 6) x =0…

A: Given : 4x = 9 (mod 5) 2x = 0 (mod 6) x = 0 (mod 4)

Q: Let X,X2 uith Parameters ----Kn bears from binomial distr'bli- n ando

A: From the given information, X1,X2,.....Xn from the Binomial distribution with parameters n and θ.…

Q: Find the or series Of x - 2x² + 3x - 4 Tray lor Series exanron about x = 2 expansion about x= 2 ed…

A:

Q: The probability that an archer hits the target is p = 0.9, so the probability that he misses the…

A: Here's it follows binomial distribution with trial 6 and probability of success 0.9 , probability of…

Q: Find, if there is any term containing x in the expansion of :

A:

Q: What is the coefficient of in the expansion of

A: Give the coefficient of x12x24x32x4 in the expansion of x1-x2-3x3+2x49

Q: Write the first four terms of the sequence {an} defined by the recurrence relation below. an +1 =…

A:

Q: Write out the first six terms of the sequence defined by the recurrence relation with the given…

A: Given:                     y0=0y1=1yn=yn-1-yn-2 for n≥2   To determine:                       The…

Q: 10 Use Binomial theorem to expand 2x .Which member contains the power x' ?

A:

Q: Find the first 4 terms of Toaylor Polyuocuial generated by fCx)= xlnx at a=2.

A: We find first four terms of Taylor polynomial generated by f(x)=xln(x) at a=2.

Q: Find manually the first three nonzero terms of the Maclaurin series expansion for f(x)= 3x+1 using…

A:

Q: show that for every positive integer n there is a prime whose decimal expansion contains n…

A: so we have to prove , for every positive integer n there is a prime whose decimal expansion contains…

Q: 3. Determine the 4th term V2m) using the Binomial Theorem.

A: To find: The 4th term of the expression 1m2-2m5 using the binomial theorem. Formula used: The rth…

Q: Calculate the number of permutations of {1,2,3,4,5,6} with three cycles (a) by using the recursion…

A: We need to calculate the number of permutations of 1, 2, 3, 4, 5, 6 with three cycles. For (a),…

Q: Use Fermat’s little theorem to find the least residue of 863 modulo 31.

A: Fermat's little theorem says: ap≡p(mod p)gcd(a,p)=1

Q: Find a Maclaurin series expansion for f(x) = cosh x

A: