() ( k k+1 П П k+1 \k=1 k+2 k=1

Q: )"-( 18 6. lim V n4n +(4n)" 2+ n2 4 4+ n2

A:

Q: Then P(X > -2) is:

A: Here use givens probability distribution table for answer the question

Q: 2. (Proof by Contradiction) For every n E Z, 4 t (n² – 3).

A:

Q: Prove n n(n + 1)(2n + 1) Σε ん? 6 k=1 for every n E N.

A: Given ∑k2k=1n=nn+12n+16, n∈N

Q: Show that (k^2 * (k+1)^2)/(4) + (k+1)^3 is equal to ((k+1)(k+2)/2)^2

A:

Q: 5. For k(x) = 3 × - 6, determine kª(8) -

A: To find the required value we need to find the value of x for which k(x)= 8. 4x/5 -6 = 8 4x= 70…

Q: (е) АПС ofreR|- ofxeR/-: o{xeR/- R-3 < x < 0 or 7 < x s o {xER-3 < x < 0 or 7 < x < 9 33x< 0 or 7 <x…

A:

Q: Prove that (1² × 2!) + (2² × 3!) + …· + (n² × (n + 1)!) – 2 = (n+ 2)! (n – 1) ... For all n E N

A:

Q: let k >= 2 show that n= 5^k-1 satisfies the equation 4σ(n) = 5n-1

A:

Q: Prove 0 + 1 + 2 + 3 + ...+ n = (n(n + 1))/2

A:

Q: Solve for n if nP, = 6nP,, where P means permutation.

A: Formula of permutation: Prn=n!n-r! We are given that P5n=6×P3n So, using the formula:…

Q: Did I prove p is not equal to 0 correctly? p is not equal to 0 by what?

A: You have proved correctly .   This can also be seen as If p= 0  Then 1/x = 0  and x= infinite or…

Q: 4. Conclude that n2 n=1 ||

A:

Q: What is the z-score if µ = 89, σ = 11.5, and x = 82? -0.61 0.79 -1.21 1.37

A:

Q: If (ar + br) 4n and n+1 k-1 E(ak - br) 1 then ar = | n+2 k-1 k-1 3 5. None 2. 72n/2

A: use elimination method Find limit for n tending to infinity.

Q: Suppose that x is N(15,4). Find the P(X>11).

A: The random variable X follows normal distribution. The population mean is 15. The population…

Q: 10. Show that È k(C) = n2"-1. Using Combinatorial Proof. k=1

A:

Q: Prove that 1-21 +2-22 + ……+n· 2" = (n – 1)2"+1+2 for any n E N. -

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Suppose that SpyBorg Inc introduces a new computer game in Houston using television advertisements.…

A:

Q: (d) For k satisfying -8 < k < k + 4 < 8, compute P(k < X < k + 4). (Round your answer to two decimal…

A:

Q: Prove (m – n)² = m² – 2mn + n² . 1.

A:

Q: in n k k-1 k (n+1\ \k-1) D+1 k+1 Pn+1 k

A:

Q: Show that n*-n3.5+300n + 234n²log n³ + nVn10 e 0(n*)

A:

Q: 5) Suppose that W1 < R" and W2 4 R". Prove (W1 n W2) < R"

A:

Q: Fix k, n E N with n > 2 and k <n – 2. Prove that: | )-(".) · ) (:) ) (^) = (":") 2 + k 2 n – 2 n n +…

A:

Q: 2. If X is N(3, o² = 4) find (a) P(X < 3). (b) P(X <5), (c) P(X < 1).

A: Given that X is Nμ=3, σ2=4 i.e. X~N(μ=3,σ=2) Then Z=X-μσ follows standard normal distribution i.e.…

Q: Prove m+n-1 Σ k k k>0 k

A: We know that  nCr=n!r!(n-r)! When k= 0, the LHS becomes 0 When k=1, the LHS becomes…

Q: If k = (0.0003,-0.0012, 0.0015,-0.0014) in R4 then -5.2||||=0.0062

A:

Q: is equal to. k=1 n2 The sum O n+1 2n O n+1 O n? +1 2n2

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Q: (-1)*-1 '(nIn n)? n=1

A:

Q: 18. Prove: n ΣΚ k = 0 = n(n + 1)(2n + 1) 6

A: The given problem is to prove the given following identity that sum of squares of first n natural…

Q: If (ar + bx) 8n and n+1 k=1 n Σ (α- br) 1 1. then ar n | n+2 k=1 k=1 O 2 None 9. 2 5 2 3 2

A:

Q: Prove n (2n = n n 1 k=1

A:

Q: 10. Suppose X-N (3.2) Find P (22}, P(X>3)

A: Given that v  X ~ N ( 3, 22 )  i.e. μ = 3 ? = 2 By using standard normal distribution we solve this…

Q: Let S = { 1 - (-¹)" | n € N}. Determine inf S and sup S. Justify. n

A:

Q: (d) Prove that 2" +3" is a multiple of 5 for all odd n E N.

A: Use the mathematical induction to prove the given statement.

Q: 2. Prove that n²(n + 1)? 13 + 23 +...+ n3 4. for n e N.

A:

Q: 2. Σ--1)k , k%3D k+1

A: The given sequence is ∑k=0∞-1kkk+1

Q: Supppose that X ~ N (2; 3). Find P (1 &lt; X &lt; 4).

A:

Q: 6. Prove o (k2) = k · Þ(k) for all k E N.

A:

Q: 04 Prove that m (n-k) = (n+1)- ("-m)n 2m n2 m 2

A: Note: Cr+1n+1=Crn+Crn-1+…+Crn-m+Crn-m-1+…+Crr→1 From identity 1, Crn-m=Crn-m-1+Crn-m-2+…+Crr Now,…

Q: (b) Z/n = (q) if and only if kq 0 for all 1 < k <n.

A:

Q: @- 8+ドy-0 K 13 let yo)=1 andyいいと Find K

A:

Q: Is 2 (n² + 6n + 9) equivalent to (2n + 6)(n + 3)? O True False

A: (1) Function ht=15+60t-16t2 Given that value t=10…

Q: 2. Suppose that P(A;) 1 for all i = 1, 2, .... Show that P(N A¡) = 1.

A: Given problem Given that

Q: B. Use combinatorial proof to solve the following problems 1. (;) (:3) = (2) (3) п-2 \k-2,

A: The formula for combination is nCr = n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)]/r!. Explanation:…

Q: 8. Working over R, suppose that M = PDP ' where P 1 Then, for any positive integer k, we have that…

A: To find Mk =?

Q: b If K = 4.1 x 10-6 then pK, Submit

A: This is a basic log problem

Q: b) Prove that 2 < (1+1/n)" < 3 for all n e N Your answer

A: Solution: Consider the given  2≤1+1nn≤3  for all n∈ℕ Let an = 1+1nn, ∀n∈ℕ Then we have to show that…

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.