6. Let fn (n = 1, 2, 3, ...) be respectively: (a) n²X[²]

Q: 50 50 51 7. + 40 39 40 • () - €) (") - () () - () () 7 8. 4 10 9. 2 10 8 8. 8 8. 10. + 2 3 6.

A: We can solve the given problem using concept of fractions.

Q: Prove let B= 6+ I %3D : m = ',2,3, 3m S. Then inf(8) =6

A:

Q: Let X-(1,0,-1,-V2)'. Then, |X|l2= Select one: a. 2 b. 1 C. 3

A:

Q: b) I =f- x(1+(In x))

A:

Q: Let n 2 2. Assume that Fn is prime. show that Fn = -1.

A:

Q: en P(x >4|X

A: Given : Probability,p = 0.5 number of trial,n = 7 Let x be the random variable that…

Q: Prove that _f₁ = = ₁+2 +851+1 −85₁-1 + ₁-2 +0(hª) 12h

A: Use taylor series expansion to prove this

Q: Let v = [1] and let z = [¹] x The Projx is equal to k k [21] where

A: Our objective is given below:

Q: 15. Find x so that m || n. (5x – 20)°

A:

Q: Suppose that q 1 is a constant. Calculate the sum n Sn = kqk = q + 2q² + 3q³ +…+nq” k=1

A:

Q: Find a given that ||a i+ (a – 1)j + (a + 1)k|| = 7.

A: Given:

Q: Show that |Z(Dn)|=1 or 2 according to whether n is odd or even

A:

Q: 81. Prove: 2+4 +6+ + 2n = n(n + 1). ...

A:

Q: 1. +1 Select one: a. th n! b. tn-1 (n 1)! C. n! tn+1 d. n! th-1 e. t+1 (n +1)!

A: Solution:-    L-11sn+1  ∵we know  that:-By using Laplace properties:-

Q: Let Sy := {1-(-1):NEN. Find iNf Sy and sup Sy

A:

Q: .1כ If n33, еxpand u %3D а'хх, a" x,x;

A:

Q: -1 15. Let A = 2 and B = Find X. A. [0 7] c5 기 В. D.

A:

Q: Let n eN 1. Show that o (n²) = ng(n) 2. Show that o (n) +

A:

Q: 6. Find f'(1) if Ax) = nx

A:

Q: Let n 2 2. Assume that Fn is prime. show that -1.

A:

Q: [ (ln(7x))²dæ

A:

Q: let  A= [23−15][23−15]. find||A||1

A:

Q: Prove that 3 | 4" – 1 where n E N.

A: To prove 3|4n -1  That is 3 divides 4n -1 for every natural number n.

Q: 2F. n 1 ;;1=2" (b), (26)

A:

Q: Let X=(1,0, – 1, - V2). Then, ||X||1= Select one: a. -1-V3 b. C. -/3 o d. 2+V2

A:

Q: Show that (an) is increasing

A:

Q: 28 X P(X=x) 2 0.10 3 0.20 4 0.30 5 0.40   P(X<4)=???        a) 0.40  B) 0.30  NS) 0.50  D)…

A: Given : The given probability distribution is X P(X=x) 2 0.10 3 0.20 4 0.30 5 0.40

Q: Show that, for n > 1 2n 1.3.5... (2n – 1),2n 2.4.6...2n n

A:

Q: (d) If each fn has fewer than M discontinuities (where M ∈ N is fixed), thenf has fewer than M…

A: To Show: If each fn has fewer than M discontinuities (where M ∈ N is fixed), then f has fewer than M…

Q: If m divides n, show that [GF(pn):GF( pm)] = n/m.

A: Given: m divides nWe need to show that GFpn:GFpm=nm

Q: 22) let XnN20, 036), iF P(X<W) = 0.05 th the value of wis

A: Given that, X~N(μ=20, σ=0.36) To find the value of W when P(X&lt;W)=0.05

Q: If m divides n, show that [GF(pn):GF( pm)] = n/m.

A: Given : m divides n . To prove : GFpn:GFpm=nm.

Q: v. Let Ac S, prove that P(Ā) = 1- P(A)

A: Given that

Q: Indicate the least integer n such that f(x) = (3æ³ + 2x²)(5æ5 + 4æ*) € O(x").

A: Finding f(x) explicitly using multiplication of polynomial. The highest power of x or degree of f…