1.7 Show that 1² +2²+ +n² -1 n(n +1) (2n + 1).

Q: Show that for every integer n, n³ + 2 is not divisible by 4.

A: Here, we use rules of divisibility.

Q: 3. (a) Use the Binomial Theorem to expand and simplify (3a²-4b)6

A:

Q: Find each (n+3)(n+2) (4n 5)(3n + 2) (n+7)(n + 5)

A: Since you have posted multiple subparts we solve the first three subparts for you to get the…

Q: How many strings of 1our decimal digits have all four digits that are different? How many strings of…

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Q: Show that 2 x ²dx (x²+1)²(x²2x+2) S 81 Z 775 50

A: FORMULAS:1.If f(x)=p(x)q(x) and degree of q(x) is greater than p(x) by atleast 2 and q(x) have only…

Q: Find the GCF of -3x3 + 15x² – 6x

A: To find the GCF of -3x3+15x2-6x

Q: 10. Use the binomial theorem to evaluate (2r³ - y) 5.

A:

Q: 21 divides 4(n+1) + 5(2n-1) whenever n is a positive integer.

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: The coefficient of x²y4z5 in the expansion of (3x+y+z)¹¹ is

A: The given expression is: (3x + y + z)11 To find: The coefficient of x2y4z5 in the expansion of (3x +…

Q: Evaluate ak+2 if ap

A:

Q: Which of the following is equivalent to 3x²(-2x)e-x² + e-x²16x O -16xe-x²(x² - 1) O 16xe-x²(x² + 1)…

A: Given query is to simplify the expression.

Q: "Co 34 "C, "C, "C; (-1)" "C, ,ne Nis equal to 10 14 (4n + 2) 2" n! 2"-n! () 3.5-7...(2n - 1)(2n +1)…

A: We have use binomial theorem  1-xn=nC0 - nC1 x + nC2 x2  + .........+(-1)n   nCn

Q: 3) (n² + 10n+18) ÷ (n+ 5)

A: To divide the following expression.n2+10n+18÷n+5

Q: 00 8tan-in Zn=1 n3D1 1+n2

A:

Q: In the expansion of (x + y)16 which term has the same coefficient as x14y2? O a. x12,4 Oc x3y14 O d.…

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Q: In the expansion of (4x + y) ^ 9, the coefficient of x3y4 is

A:

Q: 36 6 10. Find the coefficient of x³6 in (x + x² + x³ + x² + x³ + x² + x² + x³) ³

A: To find the coefficient of the term x36 in the expansion of x+x2+x3+x4+x5+x6+x7+x85.

Q: Show that whether x5 + 10x3 + x + 1 is O(x4) or not?

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Q: Indicate the least integer n such that (3x5 + x²)4 = 0(x¹). E

A:

Q: (z+1)(z+6)(z+10) z(z+2)(z+3) 3. What is the residue of at z = -2 (z+3)(z–2)² (z+2)(z+6) 4. What is…

A: 3) Given f(z) = (z+1)(z+6)(z+10)z(z+2)(z+3) Then Res(z=-2) = limz→-2(z-(-2))f(z)= limz→-2(z+2)f(z)=…

Q: 2021 2. Expand (1 + v3i)“ recall the binomial theorem.

A:

Q: (b) Show that 1 11 2 k(k + 2)(k + 4) 96 k=1

A: Given series is ∑k=1∞1kk+2k+4

Q: a) 1 (x-1)(x+2)(x+4)

A:

Q: True or False: The summation 18+28+...+n8 is a polynomial of n of degree 8.

A: Given that the summation 18+28+...+n8. The objective is to check the statement " the summation…

Q: Let A and B denote two square matrices. Then answer the following. (a) Prove that a square matrix is…

A:

Q: termine k such kx2  _ 4x + 1/2 + 0 that has real and different solution

A: To determine the value of k such that the below equation has real and different solutions.…

Q: Prove (n + 6)² – (n + 2)² is always a multiple of 8. (Use direct proof.)

A:

Q: 10 Which term of the expansion of (x²+4) ¹º contains x 20 Term number contains x 20

A:

Q: 2.x2 + 2x + 9 dr J (x – 2)(x² + 4x + 9)

A:

Q: Evaluate (z – 2)(z² + 9)

A: We have given an integral;

Q: 26. The middle term in the expansion of (x³ +4)¹0 is... A. 246,795x¹5 B. 258,048 x C. 264,897x¹5 D.…

A: As per the rules we can answer the first question and rest can be reposted.