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

Q: Let X - N(2, 4). Calculate P[X2 – 4X < 4].

A: P(X2-4X≤4)=0.7602

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

A:

Q: 2. n³+3n²-4 = 0 (n³)

A: We have used definition

Q: 5. Prove that, for n> 1, n

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Q: 4. Let A = of O 2| Calculate

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Q: what is M<E

A: Solution-As the solution is given,

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

A:

Q: Let a, b eR with a < b. Assume that a + <b - for all n E N. Show that b- = (a, b). %3D n n=1

A: We will show  two sets are equal.

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

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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: 5. Prove the following identity for n 2 1: Fzn+1 = F+1+ F;

A: We need to prove that ,  F2n + 1 = F2n+1 + F2n We know that ,   Fm+n = FmFn+1 + Fm-1Fn ,  m ≥ 1 , n…

Q: Reject Ho if |z| > N

A: We know that  Null hypothesis H0. Alternative hypothesis H1.

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

A:

Q: Let y1, . ... Yn real numbers, and let n y = 1/√ Σ² ²=1 Yi n their arithmetic mean. Show that for…

A: The proof is explained in the explanation section.Explanation:Solution: Let's prove the given…

Q: Let: A = {n € Z|0< n < 3} B = {Vn|n €Nand 1 <n < 4}

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Q: Show that for any n E N, 7(15".

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Q: Show that n 1 i2 i=1 <2 - n

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Q: Prove that E, k2* = (n – 1)2"+1 +2 for all n > 1. =D1

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Q: (1.2) Show that m m+n+1] m k=0 for any two positive integers m and n.

A: Please check the next step for detailed answer.

Q: Let X-N(65,36) P(x> 55) = O 0.5232 none O 0.9525 0.98077

A:

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

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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: 7. f : N2 → N.

A: (1) N2 ={(m,n): m,n∈N}     This is the sketch of the bijection f:N2 →N The curve which is traced on…

Q: 1. Compute the value of (), for n > 3.

A: Solution

Q: b) Evaluate UTM L{t*e- 6(t-2)}. TM

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Q: Find o e S6 such that o(1234)o = (354 6).

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Q: Show that |Z × Z|=|N|

A: ℤ represents set of integers ℕ represents set of natural numbers  To show ℤ×ℤ=ℕ We know that|ℕ|=α0…

Q: Let E = . Determine the smallest choice of N > 0 such that N. |n(n+1)|

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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: 1. Let o(n) = Edn d. Example: For primes p, q, a(p) = p+ 1. a(pq) = pq+ p+q+ 1. Show that o(n) = n…

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Q: Show that (an) is increasing

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Q: Find all n such that σ(n) = 72.

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Q: 3. Prove that 6|(9" - 3") for all n E Z+.

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Q: 3. If а, 1000". Find N E I, the set of positive integers, such that an+1 N). n!

A: Given an=1000nn!. We have to find the N∈I such that an+1&lt;an, n&gt;N. For n=1 a1=100011! For n=2…

Q: Compute (a) E-ok · k! = (n+ 1)! – 1. (b) D (") = (). k=0 TIL

A: The problem can be solved using concepts of permutation and combination.

Q: Prove that n Sk k=1 = n(n + 1)(2n + 1) 6 for all n € N.

A: To prove:We will use mathematical induction to prove this.Let

Q: 5. Algebraically show that n-1 k- = n · k k-1

A:

Q: a) Let p=13. Compute L2(3) b) Show that L2(11) = 7.

A: Here concept of field is used.

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

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Q: 1 = (₁ + - +/- ) ² (b) Prove that n < 1+ for all n € N.

A: