Induction is the method of considering certain set of statements as true and coming up with the general conclusion.
We can also compare this with the recursion in computers.
The description is:
1. Show the first element of the series is true
2. Then assume any one of the element in the series is true and prove the very next element is true.
3. Conclude for all.
The falling dominoes speaks about this:
1. The first domino falls
2. If any one of the domino falls, the next will fall
The conclusion is : All fall down.
Mathematically we says that,
First prove for n=1
Assume the result is true for n=k, and prove the result is true for n=k+1.
Then generalize it for all
one of the easiest induction problem anyone can solve is:
Sum of the positive integers =n(n+1)/2
(i.e.,) 1+2+3+…+n=n(n+1)/2
