Find all m, n E N such that: n! + 2n + 49 = m²

Q: Q3- Find the numerical value of §. xdz, if c = c, + c2 + C3.defined in the given figure. (2,2) C2…

A: We will find out the required numerical value.

Q: 2. Find an explicit formula for аn 3 За,-1+ 10ар-2 and ao %3D 0, ај 3D 7 An where

A: The solution is given as

Q: Show that if x > 9, then x³ – 8x? + 2x > 3. Show that for all n e N, if n > 10, then nª – 2n² > 3n³.

A:

Q: 2. Find p and q such that 7x+1 5 |5x-1|≤4 implies p ≤: <q

A:

Q: Find z-transfrm for (n-1) X(n) u(n-1) x (n) 5nucn) - 2 n (o.3) uci) 2)

A:

Q: 64. Find the value of n so that PQXY is isosceles. - (6n² + 7) (8n² – 11)

A:

Q: Oa, 1+ 16a, 2+ 225n for n> 2 with initial conditions ag = -23, a1 -19.

A: Given recurrance relation is  an=16an-2+225n     , n≥2 and initial conditions are a0=-23, a1=-19

Q: Prove : (A-B)n C =(A n C) -B

A:

Q: M d formulas for the entries of M", where n is a positive integer.

A: To find the power of a matrix

Q: Find a formula for sn, n > 1, if s, is given by 2 3 4 6 - - - 3' 5'7' 9 ' 11

A: We have to find Sn

Q: Z1 is a complement of Z2, and mZ1 = 23°. Find m/2. o m2

A: Given:       ∠1 is a complement of ∠2.        m∠1=23°     We know that  two angles are said to be…

Q: - such that n >r > 1, (n – 1)! r!(n – 1 – r) n! r!(n – r)! n - r -

A:

Q: for all integers n >1 E, i = n(n+1} %3D 2

A: To prove the sum of n natural numbers n≥1 is  ∑i=1ni=n(n+1)2

Q: Find the value of ‘v’ in v2 – 2v -15 = 0, if v is a natural number.

A: Given quadratic equation is,

Q: Determine whether the following is true: (a) (b) n+1 Σ₁2²= n · 2n+² + 2, i=1 n i-0 3¹ 1- 3n+1 13…

A:

Q: f in a AP the sum of m tern=ms is equal to n and the sum of n terms is equal to n then prove that…

A:

Q: Given that Z - N (0,1), find k if P(\Z| < k) = 0.8. %3D O 1.282 O -0.253 O 0.842 O -4.5

A: We have given that  Standard normal i.e, Z~N(0, 1).

Q: Find the first three terms of the expansion (4 – 2x)°. O a. 2°(1 – + + .) O b. 45(1+ 쪽 + 쪽 + ) 5x2 O…

A:

Q: use gauss's trick to determine R(n)=2+3+4+...+(n-1)+n+(n+1)

A: It is known that sum of first n numbers is n(n+1)2  that is  1+2+3+----+n=n(n+1)2 Gauss trick method…

Q: Let _X=R². Find M² if M= {(a,1)}.

A: Given that, Let X=R2 Find M⊥ if M=a,1.

Q: that Edn H(n/d)7(d) = 1 and Edn H(n/d)o(d) = n for all n, where r(n) = d(n) and σ(n) = σι (n) Σm d.…

A:

Q: Show that for all n E Z, n² 5.

A: Consider the given condition: This shows that whatever will be the values of n, it will always be…

Q: 5 Given: 21 (x + 7)º, L2 = (2x − 3). ZABC = (x²), ZD = (5x-4)° Show that ZABC= ZD. Ĉ

A:

Q: For which situation is n = EX? a. when the values of X have no duplicates b. when the values of X…

A: Solution:- We have given that,      for which situation is  n=Σ X ?

Q: Find the value of k for which A is symmetric: 1 4 3k A = 4 27 %3D 29 12 7k +1 9.

A: We have to find value k

Q: Find the mотеnt m,:

A:

Q: Find the value of n that will make each of these equations true. 1. n-7=30 2. n-6=8 3. 5n = 25 %3D n…

A:

Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: (2) Determine k such kx? – 4x +÷= 0 that has real and different solutions. 2

A:

Q: For each integer n, let Tn = {n, n2}. How many elements are in each of T2, T−3, T1 and T0? Justify…

A: Consider Tn=n,n2, where n is an integer. The objective is to find the number of elements in each of…

Q: Assume that n(U)=90n(U)=90, n(A)=41n(A)=41, n(B′)=50n(B′)=50, and n(A∪B)=63n(A∪B)=63. Find n(A∩B)

A:

Q: The sum of n,2n,3n terms of an AP are S1,S2,S3 respectively ,Prove that S3=3(S2-S1)

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Q: Q2/ prove [A] [A] = [I] if [2 4 -5 [A]= 2 7 1 3 4

A:

Q: For each integer n > 2, let P(n) bè thế för n-1 Eili +2) = n(n-1)(2n + 5) 6. %3D i=1

A: Given                   P(n):   ∑i=1n-1i(i+2)=nn-12n+56,          n≥2

Q: Use Gauss's trick to determine H(n)=1+5+9+13+...(4n-7)+(4n-3)+(4n+1) I got n(4n+2)/2 is this…

A:

Q: how many integer solutions are there to the equation  X + y + z = 10 for which  a. x,y and z + 10…

A: The positive integers are all the numbers that are greater than 0. The negative integers are the…

Q: 3. Show that a2 + b2 + c2 > ab + bc + ca and using this result show that (a) (a + b + c)2 > 3(ab +…

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Q: HW/ O Find A. B , AXB For A= (+ 3j+2K

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

Q: 5. For non-negative integer n and r, where 1<rsn, show that (n-r+1)"C,1=n(""C,). r-1

A: Given n and r non negative integers with  1≤ r≤ n. We need to prove (n-r+1)nCr-1=n(n-1Cr-1)

Q: 1. FIND ALL NUMBERS Z SUCH A23 Bz? +C2 = D 2 4 2 THAT %3D A = 13 1| T-1117 B = 124 2] 1 -2 -1 1 3 1…

A: Given A = 242131B = -1111-2-1C = 242131D = 1-1-1-121 Clearly C=AD=-B

Q: Find integers s and t so that s· 201 + t · 302 = 1 . S %3D

A:

Q: Suppose n (a)= 7a + 4, determine a such that n (a) = 39. %3D

A: GIVEN n(a) = 7a+4 and n(a) = 39

Q: If the statement is true, prove. If the statement is false, disprove. 1 + 2" > 3n for all n E Z

A: False.  take n =2

Q: Solve the recursion by substitution for  T(n)=2T(n/4)+n2 where T(1) =1

A: To solve by putting T(1)=1

Q: Assume that n(U)=70n(U)=70, n(A)=20n(A)=20, and n(B)=15n(B)=15. Then n((A∪B)′)=

A: The given details are                n(U) = 70                n(A) = 20                n(B) = 15

Q: 6. Find the length of AB in terms of n. 204 B 16 in.

A:

Q: (b) Show that V n 20 > (2i +3)3' = (n+ 1)3"+1. i=0

A: To Show- Show that ∀ n ≥ 0 ∑i=0n2i + 33i = n + 13n+1.

Q: (3b) Let n E Z. Prove that if 3|(2n² + 1), then 3 ł n

A:

Q: Evaluate if possible a) 2 ∞ Σα η=4 n2+4n+3

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.