January 18, 2017 Wednesday

Bedtime Story 

The Proof

Now let us consider the proof of the inductive step.

Which is that if the statement holds for P(0) then it must also hold true for P(k+1).

That would imply:

(0 + 1 + 2+…+ k) + (k+1) =  (k+1)((k+1)+1)/2

Now this inductive step statement will have to be proved using just the base case and nothing else.

Just how beautifully can be done

From the base case, we can write (0 + 1 + 2+…+ k) as:

k(k+1)/2 

So the left side can be written as:

 k(k+1)/2 + (k+1)

The using simple algebra:

= (k(k+1)+2(k+1))/2

= ((k+1)(k+2))/2

= ((k+1)(k+1)+1)/2

Thus we have shown that what held for P(0) also held well for P(k+1).

This is mathematical induction at it classiest. 

Mathematical induction can also be seen through a fascinating analogy.

That of a sequentially falling dominoes or as is popularly called the domino effect.

We shall take up the case of falling dominoes in the nights to come.

Stay tuned to the voice of an average story storytelling chimpanzee or login at http://panarrans.blogspot.in/

                              

Good night mon ami and my fellow cousin ape.

             

                

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Another great educator and a teacher that I am aware of is Professor Subhashish Chattopadhyay in Bangalore, India.

While I narrate stories, Professor Subhashish an electronic engineer and a former professor at BARC, does and teaches real mathematics and physics.

He started the participation of Indian students at the International Physics Olympiad.

Do visit him here:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg