You are Here: Home >< Maths

# Leibniz' Theorem watch

1. I'm going over the proof by induction.
How is;

?

Where u, v are functions of x and u^(r) is the rth derivative of u.
2. (Original post by NotNotBatman)
I'm going over the proof by induction.
How is;

?

Where u, v are functions of x and u^(r) is the rth derivative of u.
then the on top is needed in order to keep the same amount of terms.
3. (Original post by NotNotBatman)
I'm going over the proof by induction.
How is;

?

Where u, v are functions of x and u^(r) is the rth derivative of u.
I'm not sure if this is right, but you can see it if you expand the sum

Accordingly, the RHS expanded should give an equivalent expression. This might be an easier approach than using a substitution
4. To expand upon what rdk said, if you let , then you have,

5. (Original post by RDKGames)
then the on top is needed in order to keep the same amount of terms.
How comes you can have ?
6. (Original post by Desmos)
I'm not sure if this is right, but you can see it if you expand the sum

Unparseable or potentially dangerous latex formula. Error 4: no dvi output from LaTeX. It is likely that your formula contains syntax errors or worse.
\text{LHS} = \displaystyle \binom(m 0)uv^m + \binom(m1)u^2v^{m-1)+\binom(m (m-1))u^{n}v+\binom(m m)u^{m+1}
you could expand but making a quick substitution is a lot simpler.

Btw use \binom{n}{k} in latex which produces

.
7. (Original post by NotNotBatman)
How comes you can have ?
for the index,
(Original post by _gcx)
To expand upon what rdk said, if you let , then you have,

once you've changed the index you can just replace the s with s and you'll see that they are equal. Provided we do this we are not changing the value of the series.
8. (Original post by _gcx)
you could expand but making a quick substitution is a lot simpler.

Btw use \binom{n}{k} in latex which produces

.
Could you quote my post with the correct LaTeX? Cos I can't see what's wrong. And I thought of using a substitution but I didn't know if that was correct or not.
9. (Original post by Desmos)
I'm not sure if this is right, but you can see it if you expand the sum

needed } not ) around m-1
10. Thanks all, I understand it now.

(Original post by RDKGames)
then the on top is needed in order to keep the same amount of terms.
PRSOM.
11. (Original post by NotNotBatman)
How comes you can have ?
One of the properties of finite sums, you can 'shift along' a sequence of terms you're adding freely by these off-sets without altering the actual sum.

Like

and

Exactly the same result.
12. (Original post by RDKGames)
One of the properties of sums, you can 'shift along' a sequence of terms you're adding freely by these off-sets without altering the actual sum.

Like

and

Exactly the same result.
Ah, yeah, that makes sense.
13. (Original post by RDKGames)
One of the properties of finite sums, you can 'shift along' a sequence of terms you're adding freely by these off-sets without altering the actual sum.

Like

and

Exactly the same result.
We just learnt this today in uni. (Although I can't remember if this result comes up in the FP1 chapter on sums.)

Thanks RDK and _gcx and PRSOM.

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: October 25, 2017
Today on TSR

Get the low down

### University open days

• University of Exeter
Wed, 24 Oct '18
Wed, 24 Oct '18
• Northumbria University
Wed, 24 Oct '18
Poll
Useful resources

### 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

## 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