## msingh 2 years ago principle of mathematical induction

1. msingh

just one thing wanna ask why we take n=1

2. msingh

and n=k+1

3. Mertsj

The simplest and most common form of mathematical induction proves that a statement involving a natural number n holds for all values of n. The proof consists of two steps: The basis (base case): showing that the statement holds when n is equal to the lowest value that n is given in the question. Usually, n = 0 or n = 1. The inductive step: showing that, with respect to each n for which the statement holds, then the statement must also hold when n + 1 is substituted for n.

4. msingh

but we can't take n=0

5. Mertsj

So you show it is true for one value. Then show it is true for 1 more than that value. That shows it is true for all.

6. Mertsj

Not if you're using natural numbers only. Then you might want to take n = 1

7. msingh

k

8. Mertsj

Notice it says take the lowest value that n (k if you prefer) is given in the question.

9. Mertsj

Show it is true for k. Then the inductive step...show it is true for k+1

10. Mertsj
11. Mertsj

Maybe that video will help.

12. msingh

k

13. DLS

@msingh You should be polite while conversing with other people on OS and try to make some efforts for giving a proper reply followed by a thanks if a user helped you. It hardly takes your time to write "Okay" rather than k. Just an advice :]

14. DLS

Because I see @Mertsj is making a great effort to help you.

15. msingh

okay..i will keep in mind

16. msingh

@Mertsj thank u sis

17. Mertsj

I know you are thankful, msingh. You always say so and you are most welcome.

18. Mertsj

I only hope that was helpful.

19. msingh