Question

Please prove (a1+a2+……+an)^2/n ≤ (a1)^2 + (a2)^2 +……+ (an)^2.

Please prove (a1+a2+……+an)^2/n ≤ (a1)^2 + (a2)^2 +……+ (an)^2.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let n∈N, and let a1,a2,...an∈R. Prove that |a1+a2+...+an|<or=|a1|+|a2|+...+|an|
Let n∈N, and let a1,a2,...an∈R. Prove that |a1+a2+...+an|<or=|a1|+|a2|+...+|an|
Question 3. Let a1,...,an ∈R. Prove that (a1 + a2 + ... + an)2 /n ≤...
Question 3. Let a1,...,an ∈R. Prove that (a1 + a2 + ... + an)2 /n ≤ (a1)2 + (a2)2 + ... + (an)2. Question 5. Let S ⊆R and T ⊆R be non-empty. Suppose that s ≤ t for all s ∈ S and t ∈ T. Prove that sup(S) ≤ inf(T). Question 6. Let S ⊆ R and T ⊆ R. Suppose that S is bounded above and T is bounded below. Let U = {t−s|t ∈ T, s...
Find positive numbers n and a1 ,a2,...,an such that a1 + . . . an =...
Find positive numbers n and a1 ,a2,...,an such that a1 + . . . an = 1000 and the product a1 a2 . . . is as large as possible. Also prove why?
Prove this statement: Let ϕ : A1 → A2 be a homomorphism and let N =...
Prove this statement: Let ϕ : A1 → A2 be a homomorphism and let N = ker ϕ. Then A1/N is isomorphic to ϕ(A1). Further ψ : A1/N → ϕ(A1) defined by ψ(aN) = ϕ(a) is an isomorphism. You must use the following elements to prove: - well-definedness - one-to-one - onto - homomorphism
Let a1, a2, ..., an be distinct n (≥ 2) integers. Consider the polynomial f(x) =...
Let a1, a2, ..., an be distinct n (≥ 2) integers. Consider the polynomial f(x) = (x−a1)(x−a2)···(x−an)−1 in Q[x] (1) Prove that if then f(x) = g(x)h(x) for some g(x), h(x) ∈ Z[x], g(ai) + h(ai) = 0 for all i = 1, 2, ..., n (2) Prove that f(x) is irreducible over Q
(4) Prove that, if A1, A2, ..., An are countable sets, then A1 ∪ A2 ∪...
(4) Prove that, if A1, A2, ..., An are countable sets, then A1 ∪ A2 ∪ ... ∪ An is countable. (Hint: Induction.) (6) Let F be the set of all functions from R to R. Show that |F| > 2 ℵ0 . (Hint: Find an injective function from P(R) to F.) (7) Let X = {1, 2, 3, 4}, Y = {5, 6, 7, 8}, T = {∅, {1}, {4}, {1, 4}, {1, 2, 3, 4}}, and S =...
2. Exercise 19 section 5.4. Suppose that a1, a2, a3, …. Is a sequence defined as...
2. Exercise 19 section 5.4. Suppose that a1, a2, a3, …. Is a sequence defined as follows: a1=1 ak=2a⌊k/2⌋ for every integer k>=2. Prove that an <= n for each integer n >=1. plzz send with all the step
1.13. Let a1, a2, . . . , ak be integers with gcd(a1, a2, . ....
1.13. Let a1, a2, . . . , ak be integers with gcd(a1, a2, . . . , ak) = 1, i.e., the largest positive integer dividing all of a1, . . . , ak is 1. Prove that the equation a1u1 + a2u2 + · · · + akuk = 1 has a solution in integers u1, u2, . . . , uk. (Hint. Repeatedly apply the extended Euclidean algorithm, Theorem 1.11. You may find it easier to prove...
Prove that if p1, p2 are any two distinct primes and a1, a2 are any two...
Prove that if p1, p2 are any two distinct primes and a1, a2 are any two integers, then there is some integer x such that x is congruent to a1 mod p1 and x is congruent to a2 mod p2.
Let f : A → B be a function and let A1 and A2 be subsets...
Let f : A → B be a function and let A1 and A2 be subsets of A. Prove that if f is one-to-one, then f(A1 ∩ A2) = f(A1) ∩ f(A2).