What is the coefficient of z12 in (6-12z)12 O a. P(12,6)* -612 O b. C(12,0)* -(1212) O . 1212 O d. C(12,6)* -1212 O e. C(12,12)* 612

Q: 15) n(n*+5) is divisible by for each integer

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Q: Prove that 2n32n - 1 is always divisible by 17.

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Q: value of ∑n=1∞(6an+9bn) if ∑n=1∞an=8 and ∑n=1∞bn=2.

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Q: 7p The simplified product of 5m³n3 and p5 where m + 0, n # 0 and 10m4n p + 0, can be represented by…

A: We have to simplified the product.

Q: What is the coefficient of b° in the expansion of (6 -2b)17 O a. -b * C(17,9)* 29* 68 O b. C(17,8)*…

A: binomial series expansion

Q: 12 Find the term of (a – 3b)" that has b in it.

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Q: 6. A. Show that 81 – x²dx : 81n %3| 4

A: According to company rule we can answer only first question and rest can be reposted

Q: 1. Prove that 7" -1 is divisible by 6 for all n > 1.

A: As per Bartleby Guidelines we can solve only one question at a time. Hope you understand

Q: The easiest way to evaluate 2 8 5 -4 3 5 7 0 is to expand about the elements in -6

A: A square matrix is a matrix whose number of rows and columns is the same. Determinant can be…

Q: 1) Use the chain rulc to find the deriva five of fcx) = 4(-3x6+7x5)7 You do not necd to expand…

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Q: (a) In (x - 3) = 7 (b) In (x + 4) + In (x- 4) = 1

A: Given(a) In(x-3) = 7(b) In(x+4) +In(x-4) =1solve for x(a) In(x-3) = 7In(x-3) =7take Ine  both…

Q: What are the coefficients of æ5000 and æ4999 in the simplified expansion of (5æª – 2)²2021?

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Q: The factorial of n is the product of all positive integers less than or equal to n. It is…

A: Note:Hey there! Thank you for the question! We have solved this problem using trial-and-error…

Q: 18. Find MZBCA. В (5x 12)° (9x + 1)°, (10x - 37)°

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Q: 9.) Is 9" + 3 is divisible by 4? PROVE IT!

A: Given : 9n+3 is divisible by 4. To Prove: The given statement is true for n=k+1. Consider Tn=9n+3.…

Q: What is the coefficient of b° in the expansion of (6 -2b)17 O a. -C(17,8)* 29* 68 O b. -b * C(17,9)*…

A: See the details solution in below

Q: Show that 4(44!) + 49 is divisib by 47

A: Given: To show that 4(44!)+49 is divisible by 47. To explain the given statement as follows,

Q: Express the permutation (2 4 5)(1 3 5 5)(1 25) as a single cycle or as a product of cycles.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: In Z6, show that 4 | 2; in Z8, show that 3 | 7; in Z15, show that 9 | 12.

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Q: What is the coefficient of b° in the expansion of (6-2b)17 O a. C(17,9)* 29 65 O b.-C(17,8)* 29 6 OC…

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Q: Prove that 13 +23 + 23 + .. + n3 = n²(n + 1)?

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Q: Prove that AXB|=A²B² - (AB)².

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Q: 2. Prove that n = aŋɑp-1 aza,a, is divisible by 8 if and only if aza,a, is divisible by 8. A…

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Q: 4. Prove by contradiction: VmeZ, 7m+4 is not divisible by 7

A: Contrary suppose that,   m is an integer such that 7 m+4 is divisible by 7. By using the definition…

Q: Show that 3·4n+ 51 is divisible by 3 and 9 for all positive integersn

A: Consider the provided expression,

Q: Prove that 4.999...=5.000...=5

A: Proof:Let x = 4.999, then 10x = 49.99.

Q: Prove that 13n13 + 11n" is always divisible by 24.

A: Consider the given expression.

Q: 3. Show that 13" – 7ª is divisible by 6 for n > 1.

A: As per Bartleby guidelines we can solve any one question at a time. Hope you understand.

Q: prove the difference of the squares of two z integers is always divisible by 16 (i.e. z1^2 - z2^2 =…

A: We prove that (z_1)^2-(z_2)^2=16k for some integer k, then we say that divisible by 16.

Q: 2. Show that if a]b then a'|b² for all integers a and b (Symbols V, 3, A, V, V,A,→,-)

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Q: Prove that 13n13 +11n is always divisible by 24.

A: We prove this by induction on n.

Q: Find [7]^-1 in Z55 under multiplication.

A:

Q: (2) Prove that 21 + 22 = + Z2 for all 21, 22 € C.

A:

Q: 1. Show that b, = (n!)'/n > 20.

A: Consider n!1n=an1n.

Q: (a) A team of 5 debaters of IUB is to be chosen from a section where we have 6 male and 4 female…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: "For all integers n, n(n² – 1) is divisible by 6." (You may use quotient-remainder theorem and…

A: Let us consider, for all integers n a = n3 – n a = n (n2 – 1) a = n (n + 1)(n – 1)

Q: 22. Divide by (*- k): -6x-16x-5x +9 *--2. O -6x - 4x+3R 3 O -6x -4x +3 O -6x -4x + 3x R 3 -6x-4x +3x…

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Q: Find the divisors of zero in (Z12, @12, 12)-

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Q: compute the following in Z12: [9]+[11], [5]-[8], and [7][9].

A: Consider the provided question, We have to find the following in z12:9+11, 5-8, and 79 Find,…

Q: How many terms are there in the expansion of (a+4b)^20 ?

A: Given expression, (a+4b)20

Q: 6.2.2 Show that if there are 30 students in the class, and at least 2 have a last name that begin…

A: Consider the provided statement that there are 30 students in a class then at least two have last…

Q: Find the coefficient specified in each item. a) a4 in (6−1⁄2a)6

A:

Q: how is 0.46= .32276 because on the z table it's 32.64 so where does the .32276 come from

A: The z-score is -0.46.

Q: Prove that K (21-1)= { 12 (4K-1) 3

A: We have to solve given problems:

Q: The greatest common divisor of 9n + 10 and 10n +9 is Oa 10 or 19 оь. 19 O. None d. 1 or 19 Oe. 1

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Q: Fill in the blank so that the resulting statement is true.

A: Given: 3285-40-670 To get result the easiest way to evaluate 3285-40-670 is to expand about the…

Q: 7-メナ メ= t ४%= +" Find az -1/3

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Q: divisible

A:

Q: 1. Prove that 1 + Зп+2 -) = 2 an4) = (;+-) + (;+}-)+- = In3. ... = In3. - Зп+1 Зп+3,

A: