Turn on thread page Beta
 You are Here: Home >< Maths

# proof watch

1. how would I go about this? thanks
Attached Images

2. (Original post by Maths&physics)
how would I go about this? thanks
Prove the base case, assume it's true for all , prove it's true for
3. (Original post by RDKGames)
Prove the base case, assume it's true for all , prove it's true for
I did n = 1 but im stuck.

I assumed true for n = k and put into the equation both sides:

=

then, k + 1:

=
4. (Original post by Maths&physics)
I did n = 1 but im stuck.

I assumed true for n = k and put into the equation both:

=

then, k + 1:

=
EDIT: Having looked at yours for a second glance, not sure what you're doing actually. Make your logical steps clearer!

Assuming true for means that we have .

Substitute this into and rearrange to show that
5. (Original post by RDKGames)
EDIT: Having looked at yours for a second glance, not sure what you're doing actually. Make your logical steps clearer!

Assuming true for means that we have .

Substitute this into and rearrange to show that
ok, initially assumed true for n = k for both?

giving us: and .

am I right?
6. (Original post by Maths&physics)
ok, initially assumed true for n = k for both?

giving us: and .

am I right?
Why for both? You only need to assume it for the statement you're trying to prove is true. The first one is always true since that's what the sequence is defined by.

Anyway, as I said in my last post, sub your assumption into the first one and get the result.
7. (Original post by RDKGames)
Why for both? You only need to assume it for the statement you're trying to prove is true. The first one is always true since that's what the sequence is defined by.

Anyway, as I said in my last post, sub your assumption into the first one and get the result.

firstly, we need to prove the series is true and leads us to: .

so, the series: .

assume true for n = k

sub into series:

then, n = k +1 into what it leads to?
8. (Original post by Maths&physics)
firstly, we need to prove the series is true and leads us to: .

so, the series: .

assume true for n = k

sub into series:

then, n = k +1 into the series?
No...

It's actually a sequence, not a series like the question claims. They are two different things.

The sequence is iteratively defined by ... (1)

We are told to prove that the nth term is given by

Testing for we find it's true. Assuming true for we get that ... (2)

Now we wish to show that .

How? Well we know the kth term in terms of k, so we just need to use it to get the (k+1)th term in terms of k through the iterative formula (1).

So, sub (2) into (1) and show the required result.
9. (Original post by Maths&physics)
how would I go about this? thanks
Where did you find this question?
10. (Original post by Msnotorious)
Where did you find this question?
the past papers.
11. (Original post by RDKGames)
No...

It's actually a sequence, not a series like the question claims. They are two different things.

The sequence is iteratively defined by ... (1)

We are told to prove that the nth term is given by

Testing for we find it's true. Assuming true for we get that ... (2)

Now we wish to show that .

How? Well we know the kth term in terms of k, so we just need to use it to get the (k+1)th term in terms of k through the iterative formula (1).

So, sub (2) into (1) and show the required result.
thanks

Reply
Submit reply
Turn on thread page Beta

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 22, 2018
Today on TSR

### Top unis in Clearing

Tons of places at all these high-ranking unis

Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.