2. Prove that VnEN, 0 < n <1; if n > 1, then 0 < V < 1. n² n uation to prove the given

Q: 2 4) Prove that n + 5 > 4 n for all integers, n >0.

A:

Q: VI+ rdx < (2e – 1)

A: Integration in calculus is just the opposite of differentiation. We differentiate functions to get…

Q: Let yk = k", where n is a positive integer; then Ak" = (k + 1)" – k" - (1.112) nk"-+ n kn-2 +...+ 2.…

A: We have to solve given problem:

Q: Prove the identity -o (²)² = (²) using a combinatorial (counting) proof, where n, r are natural…

A:

Q: 10. Prove that (n) ≤ n/2 for n ≥ 8.

A: To prove that π(n) ≤ n/2 for n ≥ 8, where π(n) represents the number of prime numbers less than or…

Q: Let X~ N(2, 9). Compute P(1 ≤ X < 7).

A: From the provided information, Mean (µ) = 2 Variance (σ2) = 9 X~N (2, 9)

Q: Prove by mathematical induction that 1^3 + 2^3 + 3^3 + · · · + n^3 = (n(n + 1)/2)^2 for all n ≥ 1.

A: We have to prove the given statement by mathematical induction.Base Case:Let's start by verifying…

Q: Kample tetx be Let X€2Z. Prove that for cveri integer n2 , x^is cuen × is aven 2.

A: Yes, for n greater than or equal 2(n is a positive integer) if x is even then x^n will also be even.…

Q: Explain why, no matter how the circuit is completed, Pip must place an even number of additional…

A:

Q: 9. Establish the Bernoulli inequality: If 1 + a > for all n ≥ 1. (1+a)" 0, then 1+ na

A:

Q: 3.5. Let n E N. Prove that if n + ÷ < 2, then n² + n2 <4.

A:

Q: Show that it is not true that for every error 1/m there exists n such that |Ek=1 polt – r/(1 - r)| <…

A: We will show that for every m there does not exist any unique n that works for all r in (0,1)

Q: 3. Let c be a number with c 0. Then use the Binomial Formula to show that c≤nd ≤ for every index n…

A:

Q: Let Z~ N(0, 1). Find P( - 2.4 < Z < 0.9). Submit Question

A: Solution-: In this case, Z is the standard normal random variable with μ=0 and σ=1. Mathematically,…

Q: Consider certain real numbers ui and vi, i = 1,..., n, n <∞0. Show that (u₁v₁ + U₂v₂)² < (u² + u²)…

A:

Q: Let yk = k", where n is a positive integer; then Ak" = (k + 1)" – k" %3D (1.112) n = nk"-1 kn~2…

A:

Q: Use |S – SN| < bN +1 to find the smallest value of N such that Sy approximates the value of the sum…

A: According to the given information, it is required to find the smallest value of N such that SN…

Q: 3. Discrete R.V. & Binomial a.) Let X~ Bin (7, 0.3). Calculate 1.) P (X= 1) 2.) P (X 4) 4.) μ 5.) o…

A: The question is about discrete probability distribution.Introduction :Let, X be discrete which…

Q: Suppose that Z~N(0,1). Then find Pr(2.78 < Z < 2.84)

A: Given data, Z~N(0,1) That is Mean=0 Standard deviation=1 P(2.78 &lt; Z &lt; 2.84)=?

Q: 7. Prove by induction. For any n2 0, E F = F,Fn+1• k=0

A:

Q: Sp

A: The objective of this question is to understand the formula for 'n choose k', which is a concept in…

Q: exercise 1.5. Let n > 1. Prove that 6"+1 + 7"+1 6" + 7" is reduced.

A: When a mathematical statement is given to be proved for a subset of natural numbers, we use the…

Q: n + 5 > 4 n

A: We know, the square of an integer is always non-negative (n - 2)² ≥ 0 for all integers n