1+ 3k 1- 3k] 1 – 3k 1+3k 2 - prove that AK: 2 1 For A : -1 -

Q: 1. Prove that 7(x – 1) 2.

A: Let, f(x)= ex-7x+7 ,for x≥2. Differentiating both sides with respect to x, f'(x)= ex-7≥0 . This…

Q: Prove that (2k+1)! > (k+1)!(k+1)k

A: We shall prove this by induction on k. For initial step, put k=1. LHS=2×1+1!=3!=6 RHS=1+1!1+11=4 LHS…

Q: Prove that vn if n is divisible by 3 then n2+2 is not divisible by 3

A:

Q: Prove that x4+4=(x+1+i)(x+1-i)(x-1-i)

A:

Q: 2 4) The graphs of y=x and y=x make it obvious that x >x for all real number x > 1. Use induction…

A:

Q: 5. Prove OR disprove that Z/2ZOZ/3Z is isomorphic to Z/6Z

A: To prove or disprove that  Recall that , Now to prove or disprove that  These elements of these…

Q: LI) Prove that (3

A:

Q: 1- - If イ -1 provethat Kt K_9I

A: We have given that a matrix k of order 3*3.

Q: Prove by contradiction that 4* is not 0(2*).

A:

Q: 4. Prove by mathematical induction that 20+2¹ +2²+...+ 2 = 2n+1 -1.

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: then x* 1 is odd." Give a proof by contradicton to show "1fx s even integer,

A:

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

A: To prove that  L(cosh(kt))=ss2-k2

Q: Use a combinatorial argument to prove that EC(n, k) = 2". k=0

A: The Multiplication Principle If one event can occur in m ways and a second event can occur in n ways…

Q: 7. а) Prove that (ӑ — Б) х (ӑ+Б) %3 2ӑ х ѣ.

A:

Q: 2. Prove that if 5BA+ AC A - I = A, then A must be inver

A:

Q: Q4: 1- Prove that (1-0+(1+ () 0. 2. Put in the form a+ib ((1+i))- ((1-i)).

A: Here we have to prove that, 1) 1-i2+(1+i)2=0 2) Put in the form of a+ib, 1+i22-1-i22

Q: Prove that for every non-negative interger n: 2n+1 + (-1)" Σ 3· 2n i=0

A:

Q: (b) Prove by induction for all n >1 that an – bn = 2bn-1· %3D

A:

Q: 2) Prove that vnEN 12n+1 is in lowest term, i.e., prove that 30n+1 gcd(12n + 1,30n + 1) = 1 3) Vns A

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

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

A:

Q: f for ƒ : R - {2} → R- { 5} indicated by f (x) =(5x +1)/(x -2a), a bijection can be made from [0, 1)…

A: Bijective function: The domain is set A and the co-domain in set B relates elements of two sets A…

Q: integer of the form okts is also but not' conversely

A:

Q: Prove that ∀n ∈Z, gcd(7n + 1, 15n + 2) = 1 *use only the definition of divisibility and gcd please!

A: we want to prove that   gcd(7n+1 , 15n+2)=1

Q: 6. Prove that ER, # 0.

A:

Q: prove that √2+√3 is irrational

A: For rational we needed form p by q P and q are integer

Q: Prove that 1 + 4 + 7 + ... + (3n-2) = n(3n-1) / 2

A:

Q: (i) find gcd(2,3+5i) in Z[i], (ii) show that 3+4i and 4-3i are associates in Z[i] , do all , dont…

A: Solution (i)

Q: Show that if x is an integer, then gcd (x+1, x^2 -x +1) divides 3. Use this result to find knowing…

A: Solving

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) Prove that 21 + 22 = + Z2 for all 21, 22 € C.

A:

Q: Prove that Vn if n is divisible by 3 then n2+2 is not divisible by 3

A: If a and b are two integers. Suppose n is non zero integer such that |n|≠1. If a is divisible by n…

Q: Prove that 3/3 is irrational.

A: A number which can be written in the ratio , where and are integers are called rational numbers.…

Q: (3) prove That () 3

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

Q: Prove that 3+√3 is irrational.

A: As per guidelines we are supposed to solve the maximum one questions at  a time kindly post another…

Q: 2. Prove that Qn [2, 3] ~ N.

A: Two sets A and B have the same cardinality if there exists a bijection (onto , one-to-one…

Q: Prove that 2+/3 is irrational

A: Given,          To Prove : 2+3 is irrational.

Q: Prove that 0<1.

A:

Q: 4. Prove that x – 15x³ + 10x² – 21x + 2021 is irreducible in Q[x]. -

A: Given :-  Prove that x5 -15x3 +10x2 -21x +2021 is irreducible in ℚx.

Q: Prove that 2 divides a if and only if 2 divides ao. Prove that 4 divides a if and only if 4 divides…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Q: (ii) A = 82 + &V1+ 4

A:

Q: 6. By Principle of Mathematical Induction prove 6n 6

A:

Q: 6x-C), Prove that If2zf(x+ct)+Ø て

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Q: if gt2) Use induction to prove: 1 ΣΤΗ Σ 2 2n n > 0. hint: 1 2n 2 2n+1

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Q: [1+3* 1- 3k] prove that AK = 1- 3* 1+3*] |1– 3* 1+3% | - 5. For A = -1 2

A:

Q: Prove by induction: 1- 3h 27 3* 2

A:

Q: Prove that ∀n ∈ Z, gcd(7n + 1, 15n + 2) = 1.

A:

Q: Prove by contradiction that 4" is not 0(2").

A:

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

A:

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.