Welcome to Clip from Spiral logo

Interactive video lesson plan for: #10 Proof by induction prove 1+5+9+13+ +(4n-3)=n(4n-2)/2

Activity overview:

For more cool math videos visit my site at http://mathgotserved.com or http://youtube.com/mathsgotserved
Proof by induction prove 1+5+9+13+ +(4n-3)=n(4n-2)/2
mathematical induction remember that a wide collection of this can be found on mathgotserved.com before we get started with so review the plan of attack plans that we going to use to guide our problem-solving process second part so lets write it down the plan to come out plan can be broken down into three parts for number one in the base case three cases the smallest value is set of natural numbers that can satisfy the statement okay so in this problem on your deal with the set of natural numbers so in this case for the base case were going to have to show after show that n equals one's true right that's the foundation of the base case step two is the inductive hypothesis right inductive hypothesis belittling an assumption here been assumed say that an equals case trip for some and a set of natural numbers and then third part longest and sometimes most complicated part of the Om proof is the inductive step okay inductive step sibling inductive step is to show that am n equals K is true follows that work like that n equals the next step keep us one is also true rights advocate complete a little bit can be done without proof I go ahead and take a look at the proof set of him for question number 10 when the proof that prove that one is five votes nine was 13+... +4 and -3 is equal to one over two and times four and -24 all n in a set of natural numbers That's going for set to get started lets start with part 1K so what are going to show for the base case for the base case step to show on that n equals one is true alright remembered a first natural number is one of the smallest one that there is an thing to do that we going to plugging one into both sides of the equation we have four and -3 is equal to one half and transport and -2 so plug-in wireless I will have 4×1-3? Is it equal to 1/2×1×4×1-2 is a true statement or not sort this out with employees for -31 is one equal to 1/2×4×1 is 4-2 is to just advice to the device further you have is one equal to one and the answer is yes so our base case is sound right let's move on to our home inductive hypothesis supported inductive hypotheses we're going to be making an assumption about assume assume that n equals K true for some K in the set of all natural numbers alright let's assume that that's true the what does that look like always going to do here is plug-in K for n in the original problem of Casey's's original problem right here we're going to plugging k for 'n both sides of our equation so that that look like this to the maker subject assume change, there on assume that that all the statement is one was five
+13+... Plus the 24 and -3

4K -3 is equal to one half times K times 4K -24 song K in the set of natural numbers are okay to Dennis R inductive hypothesis
in the inductive step further. The inductive step the hard part inductive step number going to do here for inductive step we want to show that it n equals K is true that follows that n equals the next step is keep us one is also true right to prove that the next it is true using this assumption of the important of your arguments are external links start by writing the left side of this statement of problem and it was limiting the next step case of right and left sides looking to have one spine.
+13+... Plus 4K -3 next step is lost for step four is bit of him K within a half people is one -3 I now is going to use our inductive hypotheses here to make a substitution rights alone substitution was going to make this piece of our inductive step right near begin substituting with another value that we stated with equal to our inductive hypothesis we know that this entire expression is equal to one half key times 4K -2 rights... On the best substitution here so this is that equal to the equal to one half K times 4K -2 advocate simplifies a little bit +4 times K okay 4×1 is 4-03 use one of one there edited the site appear by assumption in part 2O making his or assumption to I now select go ahead and that simplify this a little bit further selecting what can we do here well you noted to me come I will life easier is good to how idea what the target is okay; make note of what the target should look like it, simplify individual format easy to write back the page so what is our destination results going to be so while it's that look like is the right part of her inductive step with all Kay's replacement keep us what so what better look like we can have one half is the type of target is one half times into an output keep us one times for times cases 1-22 this is what I want this and expression to simplify into okay it's good to do this we can have idea how to manipulate you are expression to get your initial here intended target is anything but a little bit more so I can have all an easy expression to intellect

Tagged under: 5^-2^ divisible 3,^3+2n divisible 3,8^-1 divisible 7,1/(1X2)+1/(2X3)+...+1/((+1))=/(+1),^2 than2n,8+2x8+3x8+..+8n=,1+3+5+7+...+(2n-1)=^2 N,sum ^2= 1/6n(+1)(2n+1),9^-2^ id divisible 7,1+5+9+13+..+(4n-3)=½(4n-2), Σ =(+1)/2,1^3+2^3+3^3+..+^3= ((+1)/2)^2 ^2(+1)^2/4,10^1+10^2+10^3+ +10^ = 10/9(10^-1),derivative ^-1 ( (-1)^ !)/ ^(+1),2^ greater equal 1+,3^ thatn (+1)!

Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.

Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip

Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans

Play this activity

1. Students enter a simple code

2. You play the video

3. The students comment

4. You review and reflect

* Whiteboard required for teacher-paced activities

Share on:

Share #10 Proof by induction prove  1+5+9+13+  +(4n-3)=n(4n-2)/2 on Google+ Share #10 Proof by induction prove  1+5+9+13+  +(4n-3)=n(4n-2)/2 on Twitter Share #10 Proof by induction prove  1+5+9+13+  +(4n-3)=n(4n-2)/2 on Facebook Pin #10 Proof by induction prove  1+5+9+13+  +(4n-3)=n(4n-2)/2 Email #10 Proof by induction prove  1+5+9+13+  +(4n-3)=n(4n-2)/2

Ready to see what else Spiral logo can do?

With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.

Quickfire

Carry out a quickfire formative assessment to see what the whole class is thinking

Discuss

Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices

Clip

Turn any public video into a live chat with questions and quizzes

1000s of teachers use Spiral to deliver awesome, engaging activities that capture students' understanding during lessons.

Now it's your turn Sign up

Spiral Reviews by Teachers and Digital Learning Coaches

Spiral
Review of Spiral by teacher: Kathryn Laster @kklaster

Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech

Spiral
Review of Spiral by teacher: Room 220 Math Stars @3rdgradeBCE

Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks.

Spiral
Review of Spiral by teacher: Miss Ord @ordmiss

Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral

Spiral
Review of Spiral by teacher: Adam J. Stryker @strykerstennis

Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks!

Spiral
Review of Spiral by teacher: Dr Ayla Göl @iladylayla

A good tool for supporting active #learning.

Spiral
Review of Spiral by teacher: Brett Erenberg @BrettErenberg

The Team Up app is unlike anything I have ever seen. You left NOTHING out! So impressed!

Get the Clip Chrome Extension & Create Video Lessons in Seconds

Add Clip to Chrome