Question

****Please show me 2 cases for the proof, one is using n=1, another one is n=2,...

****Please show me 2 cases for the proof, one is using n=1, another one is n=2, otherwise, you answer will be thumbs down****Hint: triangle inequality. Don't copy the online answer because the question is a little bit different

use induction prove that for any n real numbers, |x1+...+xn| <= |x1|+...+|xn|.

Case1: show me to use n=1 to prove it, because all the online solutions are using n=2

Case2: show me to use n=2 to prove it as well.

Homework Answers

Answer #1

If there is any problem in understanding please comment! Thank you ?

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
proof by induction: show that n(n+1)(n+2) is a multiple of 3
proof by induction: show that n(n+1)(n+2) is a multiple of 3
Consider a sequence defined recursively as X0= 1,X1= 3, and Xn=Xn-1+ 3Xn-2 for n ≥ 2....
Consider a sequence defined recursively as X0= 1,X1= 3, and Xn=Xn-1+ 3Xn-2 for n ≥ 2. Prove that Xn=O(2.4^n) and Xn = Ω(2.3^n). Hint:First, prove by induction that 1/2*(2.3^n) ≤ Xn ≤ 2.8^n for all n ≥ 0 Find claim, base case and inductive step. Please show step and explain all work and details
Can someone solve these for me? 1.) Show that (F_(n-1))(F_(n+1)) - (F_n)^2 = (-1)^n for all...
Can someone solve these for me? 1.) Show that (F_(n-1))(F_(n+1)) - (F_n)^2 = (-1)^n for all n greater than or equal to 1. (F_n is a fibbonaci sequence) 2.) Use induction to prove that 6|(n^3−n) for every integer n ≥0
DISCRETE MATHEMATICS PROOF PROBLEMS 1. Use a proof by induction to show that, −(16 − 11?)...
DISCRETE MATHEMATICS PROOF PROBLEMS 1. Use a proof by induction to show that, −(16 − 11?) is a positive number that is divisible by 5 when ? ≥ 2. 2.Prove (using a formal proof technique) that any sequence that begins with the first four integers 12, 6, 4, 3 is neither arithmetic, nor geometric.
Consider the sequence (xn)n given by x1 = 2, x2 = 2 and xn+1 = 2(xn...
Consider the sequence (xn)n given by x1 = 2, x2 = 2 and xn+1 = 2(xn + xn−1). (a) Let u, w be the solutions of the equation x 2 −2x−2 = 0, so that x 2 −2x−2 = (x−u)(x−w). Show that u + w = 2 and uw = −2. (b) Possibly using (a) to aid your calculations, show that xn = u^n + w^n .
Please note n's are superscripted. (a) Use mathematical induction to prove that 2n+1 + 3n+1 ≤...
Please note n's are superscripted. (a) Use mathematical induction to prove that 2n+1 + 3n+1 ≤ 2 · 4n for all integers n ≥ 3. (b) Let f(n) = 2n+1 + 3n+1 and g(n) = 4n. Using the inequality from part (a) prove that f(n) = O(g(n)). You need to give a rigorous proof derived directly from the definition of O-notation, without using any theorems from class. (First, give a complete statement of the definition. Next, show how f(n) =...
Show that for all positive integers n ∑(from i=0 to n) 2^i=2^(n+1)−1 please use induction only
Show that for all positive integers n ∑(from i=0 to n) 2^i=2^(n+1)−1 please use induction only
Let f : R \ {1} → R be given by f(x) = 1 1 −...
Let f : R \ {1} → R be given by f(x) = 1 1 − x . (a) Prove by induction that f (n) (x) = n! (1 − x) n for all n ∈ N. Note: f (n) (x) denotes the n th derivative of f. You may use the usual differentiation rules without further proof. (b) Compute the Taylor series of f about x = 0. (You must provide justification by relating this specific Taylor series to...
1. One-Way ANOVA Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent...
1. One-Way ANOVA Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent Opinion * Community 96 100.0% 0 0.0% 96 100.0% Opinion * Community Crosstabulation Community Total A B C Opinion Against Count 18 7 15 40 Expected Count 17.5 9.2 13.3 40.0 For Count 12 6 5 23 Expected Count 10.1 5.3 7.7 23.0 NoOpinion Count 12 9 12 33 Expected Count 14.4 7.6 11.0 33.0 Total Count 42 22 32 96 Expected Count 42.0...
Two identical sealed containers (1 and 2) are connected to one another by a narrow tube...
Two identical sealed containers (1 and 2) are connected to one another by a narrow tube with a valve. Initially, the valve is closed, container 1 is filled with a fluid, and container 2 is empty. Both containers have a ruler taped to their sides in order to measure the height of any fluid they contain. A) . When the valve is opened for a time interval Δt, the level of the fluid in container 1 drops by 3 cm....
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT