Mathematical induction Definition and 215 Threads

It seems to me that sometimes mathematical induction can be a lazy alternative to a real proof. I am bothered by the fact that induction does not tell you why something works, nor can it help in the actual derivation of formulae. Am i right in throwing it away so quickly? It just seems...

The question is: Prove by mathematical Induction that f(n) \equiv 2^{6n}+3^{2n-2} is divisible by 5. This is what I did: Suppose that the given statement is true for n=k Since the f(k) is divisible by 5, f(k)=5A (where A are is a constant.) Also, from the given statement...

Show taht for every natural numbers n>=2 n \geq 2 the number 2^2^n - 6 2^{2^n} -6 is a multiple of 10. Using mathematical induction. Okay i got no clue how to start this question. Ahhh Is there a series where the x^n is a series? Well this stuff really sucks.

I've been working on this problem for the past two and a half hours. The problem is: Prove by induction that n^3 + 2n is divisible by 3 for non-negative integer values of n. No matter how I try, I cannot manipulate the expression of the inductive step so that it is divisible by 3. I have...

Question Suppose a,d \in \mathbb{Z} and consider the arithmetic sequence \{a+kd\}_{k\in\mathbb{N}\cup\{0\}}. Use the Principle of Mathematical Induction to prove that \sum_{k=0}^n a+kd = \frac{1}{2}(n+1)(2a+nd)

I was told that the following can be proven by induction. Can someone explain to me how this can be done? I also have the following fact: If p|(ab) then either p|a, p|b or both. Let p be a prime number and let a_i, i = 1,2,3,...,n be integers. If p|(a_1)(a_2)...(a_n) then p divides at...

2 math questions (summation, mathematical induction) I have 2 questions regarding summation and mathematical induction 2. Prove by mathematical induction \sum^n_{r=1} \frac {1}{r(r+2)} = \frac {3}{4} - \frac {(2n+3)}{2(n+1)(n+2)} i am now trying to prove that 3/4 -...

Hi I was wondering if any of you could explain the concept of Mathematical Induction to me...I really am confused on this, we didn't learn it in class (yet we're going to be quizzed on it)...if you could walk through a simple example, it would be really appreciated...thank you!

i was having trouble coming up with an induction proof for this problem, although i have tried and was able to prove it sumhow(using numbers 1 n so forth, teacher doesn't allow us to use them yet), but not using induction. I have no clue on how to do this using induction. please help me...

how to prove : the product of n consecutive positive integers is divisible by n! by using Mathematical induction , you can assume nCk is an integer ?? it is in urgent , please help , thank you! :smile:

Guys, I'm trying to prove by induction that the sequence given by a_{n+1}=3-\frac{1}{a_n} \qquad a_1=1 is increasing and a_n < 3 \qquad \forall n . Is the following correct? Thank you. :smile: Task #1. n = 1 \Longrightarrow a_2=2>a_1 is true. We assume n = k is true. Then...

Here's an unsolved problem I found in my Algebra book. See if you can spot where the error in reasoning lies: A serial killer is sentenced to be executed. He asks the judge not to let him know the day of the exectuion. The judge says: "I sentence you to be executed at 10 A.M. some day of...

Hi, I'm looking for some help regarding a problem I have. It's a problem I'm doing for my computer science class, and we need to prove certain conjectures using mathematical induction. Now, I've never learned mathematical induction in any class, so I'm basing everything I know about it off...

I have a question about mathematical induction, I know that this stuff is really easy I just can't seem to get the point here. I lost a lot of math alegbra more likely to say because of moving and now I am having trouble with algebra in my first semester of college. I don't really need anyone...

Induction Hypothesis: In fact pa is true for all integers n greater than a particular base value and you should complete the proof given below to use the principle of mathematical induction to prove this. pa : n-2 < (n^2 – 3n)/12 Base case is n = 14 Because: n-2 < (n^2 – 3n)/12...