19.The expansion of 1- x) = X. 1- 4x + 7x2 C.1-4x- 7x² - .. B. 1+4x- 7x² + D. 1+4x + 7x² + ... ... .. uhen

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 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>

A:

Q: Why is it that if I do row expansion on the first row, I get det(A) = -1, but, if I do it in the…

A: We need to find the determinant of a using the first row expansion and as well using the second…

Q: 1 Prove that 1+2+3+..+n = +1) hy proof of mathematical induction.

A:

Q: Determine the term involving y5 in the expansion of (3y +).

A: Please refer the attached image for complete solution. THANK YOU.

Q: The first term of the expansion of (j – 3n)a is –-3nª. True or False?

A: The \displaystyle \left(r+1\right)\text{th}(r+1)th term of the binomial expansion of \displaystyle…

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 Prove 2.5 1 1 + .…+ 8.11 1 for n > 1. %3D 5.8 (3n-1)(3n+2)

A: Prove S(n) for n=1.   LHS =1/2.5 =1/10; RHS = 1/6+4=1/10   So it is true for n=1.

Q: 4. Find the coefficient of the term containing x' in the expansion of (x-2y)“.

A:

Q: THEOREM 2.4 The number of distinct permutations of n things of which n1 are of one kind, n2 of a…

A: Given: Theorem 2.4 and Theorem 2.5

Q: 3. Show that if n = 3 mod 4, then n cannot be the sum of squares of two integers.(i.e there are no…

A:

Q: 1. Prove by induction: 22 + 1*3 12 n2 а. п(п+1) + (2п-1)+(2n+1) ... 3*5 2(2n+1)

A:

Q: Compute [5]-l© [12] in Z17.

A: The solution is 16. (Detail is given in the handwritten notes.)

Q: 4. Find the expansion of (x + y)6 using Binomial Theorem.

A:

Q: R² = gen gen

A: see below the reason

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

A:

Q: 2. Prove that L(cashkt)= ki 52-K2

A: To prove that  L(cosh(kt))=ss2-k2

Q: Find the term containing x in the Expansion of (x +3 y)*

A:

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: Suppose a, n E Z and 0 < a< n. Prove that ()- (":")- (:-) n - 1 %3D + a a а- 1 in two different…

A: Given a,n∈ℤ such that 0&lt;a&lt;n. (1) Consider:…

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…

A:

Q: 8. The Laurent's expansion of (2² – 1) (2² + 4 for |z|<1 is 5z2 2125 1). 4 64 16 2) + 21 4 4 4 3) -…

A: None of the option 1,2,3 and 4 is correct. Please check it.

Q: Prove 2- = =4 has infinite many Solu thans ZEC.

A:

Q: Proceed as in Example 3 in Section 6.1 to rewrite the głven expression using a single power serles…

A: Given ∑n=2∞nn−1cnxn−2+∑n=0∞cnxn+2 We have to rewrite the given expression using a single power…

Q: a)Show by one combinatorial method that: 2 2 n C) - () - (") 2n +... + 2 n

A: Given information: The following identity is provided: n02+n12+n22+................+nn2=2nn It is…

Q: 4) Find the Term that free from x of the expansion (x2 +10

A: Use binomial expansion:-

Q: 3. Find the expansion of (x + y)$ using Binomial Theorem.

A: The solution is given as

Q: 7. Show that 1 En(ln n)P if and only if p> 1.

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

Q: (8) Prove that if A and B are similar, then their transposes are also similar.

A:

Q: п(п + 1) Show that , k 2 k=1

A:

Q: Evaluate the integral

A: Consider the given integral value. Substitute t = 3 sec u. Differentiate t w.r.t u and calculate dt.…

Q: 7. Prove that 2. O = (-1). %3D

A:

Q: 2. Prove by the Principle of Mathematical Induction that 5-2 + 5-4 + 5-6 +... + 5-2n = 24-'(1 –…

A:

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: (3) prove That () 3

A: We have to use z = x + iy.

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

A:

Q: 15 Use the Binomial Theorem to expand: 2x 80x4y , 80x³y?, 40 10 A. 32x+ 3 9 27 + 81 243 80x4y, 160…

A:

Q: 3) Find the Term that includes x? of the expansion (x +

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

A:

Q: Find the term independent of x in the expansion of 3 1 - 2r

A:

Q: Obtain the expansion of : 2 up to the term in x8 1-3x2

A:

Q: 4. The term in x* in the expansion of (1-x+x)1- 6. is: | .2 A. x* R 15 16 15 115 25 xD.x+ 4 - - 4 16…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Obtain the expansion of ; up to the term in x* 1-3x2

A: We know 11-x = 1+x+x2+x3+ ⋯

Q: Show that on finite m

A: To prove that on finite measure, Lpand almost everywhere convergence are independent.

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

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.