1. Prove the following results using the definition of |- and the triangle inequality. For n N and 9₁, 92,..., Un ER, 31 +32+...+yn|≤|y1| + |32|+ .+|ynl. Hint. Use induction.

Q: Find the length s of the path (3 + 10r,9 + 2r312) over the interval 5 < t < 6.

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Q: Prove: | a | - | b | &lt;= | a + b |

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Q: 8. Let a₁ ≥ a2 ≥ ... ≥ an and b₁,b2,..., bn be two sequences of non-negative real numbers such that…

A: The given problem is to prove the given inequality for the given two sequences an and bn and…

Q: Show that 1+2+3+… +n = (";").

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Q: If | B| = m then n

A: We know that, If there are n elements in a set A, then there exists 2n subsets of A. The power set…

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

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Q: P(X=x) 0,10 0,20 0,30 0,40 P(3 < X S4 )= ??? O A) 0,10 O B) 0,40 C) 0,30 O D) 0,50 XN34 5

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Q: Use algebra to find the largest possible value of 8 or small- est possible value of N that makes…

A: 23. This equation comes from the ε,δ definition of the limit. As x→2 the function 3x-1→5. So for all…

Q: Prove the following inequality п(п — 1) (1+ x)" 21+ nx + x², r20 2 for any n > 1.

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Q: Let f AB, prove the following: (a) if S, T are subsets of A, then f(SNT) ≤ f(S) nf(T); (b) if U, V…

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Q: 7. (12 points) Use a proof by contradiction to prove: For all sets A, B, and C (A\C)n(B\C)n(A\B) = 0

A: Step 1: proof  let (A/C)∩(B/C)∩(A/B)=Φ this means ∃x∈(A/C)∩(B/C)∩(A/B) Step 2:⇒x∈A/C,x∈B/C,x∈A/B…

Q: Cive a poof by Pnduction of the followfng sietement. शिरकुणार्थ If 31 a positane प्ठफा ् गेत (५+)…

A: Solution

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: * 30. Let n and k be integers with 1 ≤ k ≤n. Show that n Σ() ( k=1 k n - 1) = (2n+2)/2 - (2n).

A: The answer for the given questions has been solve step by step below please find the attachments…

Q: Which of the following rule is defined as "the sum of the first and last ordinate, twice the sum of…

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Q: mutually disjoint? Why or why not?

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Q: b) Prove that 3abc ≤ a³ + b³ + c³ for nonnegative a, b, c. (Hint: In the in- equality of part (a),…

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Q: Please

A: We know that, Statement: If P then Q. Contrapositive: If ~Q then ~P.

Q: Provide answers in interval notation. 18) x2 – 5x s -4 x2_5x

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 3. For all sets X, Y and Z, prove the given statements by the indicated method. (a). Method of…

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Q: Lise a direct proof to show "fx's odd and y is even, anen x+1s odd."

A: The given statement is: "If x is odd and y is even, then x+y is odd" Result: Any odd number x can be…

Q: 3. Prove the triangle inequality: For any real numbers x, y, |x + y ≤ |x| + |y].

A: For any real number  we have to prove

Q: Let a₁,..., an EC with |aj| < 1 for all j = 1,...,n and A₁,..., An ≥ 0 real numbers satisfying 1 j =…

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Q: In Intérval notation. 2 sx < 10 A) [2, 10] B) [2, 10) C) (2, 10] D) (2, 10) the problem. 10 The…

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Q: 19. Use the Archimedean Property of R to prove that if z, M are real numbers such that 0≤x≤ for…

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Q: Prove: For c &gt;= 0 , | a | &lt;= c if and only if -c &lt;= a &lt;= c

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Q: Exercise 6.6. Let the inductive set be equal to all natural numbers, N. Prove the following…

A: As per our guidelines only first three subquestions are solved. For remaining subquestions kindly…

Q: 1. Show that if P(A) > 0, then P(AB|A) > P(AB|AUB)

A: Show that if P(A) &gt; 0 thenP(AB|A) &gt; P(AB|AUB)

Q: Q: State whether the following statements are true or false: 1. Let S be a non-empty subset of the…

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Q: Suppose b1 + *+ bm < n. Prove that b,!bm!< n!.

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Q: Let Xipnnig Xu~N(Po²). Find Consistent estimator of M using a chebychev's inequality.

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Q: Let a₁ ≥ a2 ≥ ….. ≥ an and b₁,b2, ..., bn a1 b real numbers such that for each k, 1 ≤ k it ant

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Q: 1. Apply the AM-GM inequality to prove that for any n = N, (n + 1)" ≥ 2nn!.

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Q: the suprema and infima of the following sets: (a) {n EN n² < 10}; (b) {mn|m, n€ N}; n (c) {2+1 n €…

A: Since you have posted multipart question and we can answer three subparts. So, answered the first…