You are Here: Home >< Maths

# FP1 Summation Series where r=0 watch

1. I really need help with summation series where r=0. How does this affect the formulas? Also, what do you do when 'n' is featured in the summation series (mixed in with the r-values).

To be more specific, question 10ii in the Edexcel June 2013 (R) paper is where I'm really baffled, I don't understand the mark scheme either

If anyone could please explain this, I would be eternally grateful!

Paper: https://7cba9babeb0db0ff9468853e0b2d...%20Edexcel.pdf

Mark Scheme: https://7cba9babeb0db0ff9468853e0b2d...%20Edexcel.pdf

p.s. I really this question was asked previously, but I didn't understand the explanation at all and it's quite old now
2. Hi

r=0 problem:

The standard formulae only apply when r=1.

Therefore, if the summation given starts with r=0, work out the first term 'manually' by subbing in r=0 and then add the sum from r=1 to n.

This is just like how you might do a proof for a summation: when you have a sum from r=1 to n=k+1, you do the sum from r=1 to n=k and ADD the r=k+1 term 'manually',

n in the formula problem:

just like how you might get a 'show that' question for a summation and you separate out each component in the formula, do the same. by this i mean, you currently have sum (r^2 -2r +2n +1). Separate this to give: sum (r^2) - sum (2r) + sum(+1) + sum (2n)

For sum (2n), it's just effectively 2n + 2n + 2n +...+ 2n, n times, so sum(2n), is 2n^2,

Hope this helps. if you need clarification, feel free to ask
3. (Original post by Horagontus)
I really need help with summation series where r=0. How does this affect the formulas? Also, what do you do when 'n' is featured in the summation series (mixed in with the r-values).

To be more specific, question 10ii in the Edexcel June 2013 (R) paper is where I'm really baffled, I don't understand the mark scheme either

If anyone could please explain this, I would be eternally grateful!

Paper: https://7cba9babeb0db0ff9468853e0b2d...%20Edexcel.pdf

Mark Scheme: https://7cba9babeb0db0ff9468853e0b2d...%20Edexcel.pdf

p.s. I really this question was asked previously, but I didn't understand the explanation at all and it's quite old now
when 'n' is featured in the summation series (mixed in with the r-values).
just multiply the formula by n
4. (Original post by Salzy)
when 'n' is featured in the summation series (mixed in with the r-values).
just multiply the formula by n
how does this help?
5. Yeah what Amar says, only thing I do slightly differently is instead of taking out the 2n term from the (r^2 - 2r +2n + 1), you can treat the (2n+1) term the same as you'd treat any other constant. Normally, the sum from r=1 to n of a constant k would be kn, so the sum from r=1 to n of (2n+1) is n(2n+1)

In this question, it is the sum from r=0 to n. As Amar said, you can just treat it like it is from r=1, then put 0 into the r equation to get the term when r=0 then add it on to the sum from r=1 to n, which would give you the the sum from r=0 to r=n

When you put in 0 to any equation, the value you will have will always equal the constant on the end of the r equation, here out constant is (2n+1). This means you can use the formula as normal to get your sum of the r^2 and -2r terms, then for the (2n+1) you have n(2n+1) as shown in the 1st paragraph, then you have an extra constant added on from when r=0, as shown in the 2nd paragraph, meaning that for the constant you have n(2n+1) + (2n+1) = (n+1)(2n+1)

This can be used anytime it is the sum from r=0, you use the formula as normal but instead of the sum of any constant k being kn, it will be k(n+1) to account for the addition of the 0 term.

Hope this helps, did that question just now!
6. (Original post by AmarPatel98)
Hi

r=0 problem:

The standard formulae only apply when r=1.

Therefore, if the summation given starts with r=0, work out the first term 'manually' by subbing in r=0 and then add the sum from r=1 to n.

This is just like how you might do a proof for a summation: when you have a sum from r=1 to n=k+1, you do the sum from r=1 to n=k and ADD the r=k+1 term 'manually',

Hope this helps. if you need clarification, feel free to ask
When you "manually" obtain the value of r=0, does anything happen to the n at the top? i.e. would I have to use (n-1) rather than n as the sequence is reduced by one component?

7. (Original post by Horagontus)
I really need help with summation series where r=0. How does this affect the formulas? Also, what do you do when 'n' is featured in the summation series (mixed in with the r-values).

To be more specific, question 10ii in the Edexcel June 2013 (R) paper is where I'm really baffled, I don't understand the mark scheme either

If anyone could please explain this, I would be eternally grateful!

Paper: https://7cba9babeb0db0ff9468853e0b2d...%20Edexcel.pdf

Mark Scheme: https://7cba9babeb0db0ff9468853e0b2d...%20Edexcel.pdf

p.s. I really this question was asked previously, but I didn't understand the explanation at all and it's quite old now
I think someone's method on here is the same as mine - which I got from Zacken, where you take the 2n+1 term out. You can refer to the post here. http://www.thestudentroom.co.uk/show...955045&page=19
8. (Original post by TommyBrecon)
When you "manually" obtain the value of r=0, does anything happen to the n at the top? i.e. would I have to use (n-1) rather than n as the sequence is reduced by one component?

Nope you wont.

Let me put it this way to make it clear:

When the sum is from r=0 to r=n, the series is: (r=0 term) + (r=1 term) + (r=2 term) + ... + (r=n term)

When we do it 'manually', we do: (r=0 term manually) + (sum from r=1 to n) = (r=0 term) + (r=1 term) + (r=2 term) + ... + (r=n term)

We break it up so we can use the standard formulae.

Hope this makes sense
9. (Original post by Nikhilm)
Can you not be so passive aggressive.
stop trolling

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: May 19, 2016
Today on TSR

### The most controversial member on TSR?

Who do you think it is...

### Is confrontation required?

Discussions on TSR

• Latest
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
Discussions on TSR

• Latest

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