Mathematical Induction

Mathematical Induction is a good way to start writing proof for beginner too. Mathematical Induction is usually read by students at post-secondary level(Diploma/A-level). Problem is, equations are given to you and you just have to prove is true. As a real problem solver, you should explore more and able to create without memorizing!

Example:
Before we prove (k+1) .. lets find out why .

If you add the very last number to the first, then move the 2nd last to the 2nd and so on, the result will be ...

Sum them up:

Result :

Since 2 integers being sum together, we divide them by 2 so, created. Now you can prove (k+1) for
Now you can prove for (k+1) easily.

Another Example: Let's explore further for . Lets say you can't remember. Time to think creatively and do real math.

Lets see ..

Divide them

Finally, divide the denominator and numerator

Can you see the above number pattern? the numerator are odd integers while denominator are constant 3. Therefore,




created!

Now you can prove (k+1) for