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# FP1 - proof by induction watch

1. I don't understand how to do proof by induction:
the question im stuck on is;

(the sum of) (3k+1) =1/2n(3n+5)

PLEASE HELP SOMEONE
2. (Original post by Amyherdman)
I don't understand how to do proof by induction:
the question im stuck on is;

(the sum of) (3k+1) =1/2n(3n+5)

PLEASE HELP SOMEONE
Have you tried it yet?
3. (Original post by edothero)
Have you tried it yet?
yes but i dont know how to do it
4. (Original post by Amyherdman)
yes but i dont know how to do it
Remember the 4 steps.
Prove for n=1
Assume true for n=k
Let n=k+1 and prove
Conclusion

What step are you stuck on?
5. (Original post by edothero)
Remember the 4 steps.
Prove for n=1
Assume true for n=k
Let n=k+1 and prove
Conclusion

What step are you stuck on?
mainly assume true for n=k
6. (Original post by Amyherdman)
mainly assume true for n=k
As far as I'm aware, for this part you just need to write a statement saying you assume its true for n=k? There's not much more you need to do for this step..
Would be good if you could post your working out

Zacken can take over here. I have a Physics exam to revise for
7. (Original post by Amyherdman)
mainly assume true for n=k
Yeah, all you need to do here is just write down Assume true for n=m, so that we have:

That's it.

(Original post by edothero)

Zacken can take over here. I have a Physics exam to revise for
Argh, trying to do S3 but I'll take over.
8. (Original post by edothero)
As far as I'm aware, for this part you just need to write a statement saying you assume its true for n=k? There's not much more you need to do for this step..
Would be good if you could post your working out

Zacken can take over here. I have a Physics exam to revise for
thank you, ive done that but thought i had to do more to help me prove n=k+1
9. (Original post by Amyherdman)
mainly assume true for n=k
Write the statement in k rather than n, not too difficult.
10. (Original post by Zacken)
Yeah, all you need to do here is just write down Assume true for n=m, so that we have:

That's it.

Argh, trying to do S3 but I'll take over.
what about n=k+1 then??
11. (Original post by zetamcfc)
Write the statement in k rather than n, not too difficult.
thats what i did but i thought there was more than that to do, how do you do n=k+1 then?
12. (Original post by Amyherdman)
what about n=k+1 then??
Then, for n=k+1, we want to prove that:

- we want to prove this equality somehow, so let's start from the sum:

- you've assumed something about the sum to k, maybe plug it in and do some factorising to prove what we want to prove?
13. (Original post by Amyherdman)
thats what i did but i thought there was more than that to do, how do you do n=k+1 then?
Zacken will help, got stuff to do.
14. Hint: The sum to k+1 = The sum to k + the (k+1)th term. Now substitute for the sum to k with the inductive hypothesis (the assumption that the statement is true for n=k).

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