You are Here: Home

FP1: Series homework help

Maths and statistics discussion, revision, exam and homework help.

Announcements Posted on
Find out how cards are replacing warnings on TSR...read more 03-12-2013
1. FP1: Series homework help
I'm currently struggling on a 'show that' series question, i appreciate any help.

The question, 'Show that \displaystyle \sum ^{n}_{r=1}r(2r+1) = 1/6n(n+1)(4n+5)
2. Re: FP1: Series homework help
(Original post by BigCal007)
I'm currently struggling on a 'show that' series question, i appreciate any help.

The question, 'Show that \displaystyle \sum ^{n}_{r=1}r(2r+1) = 1/6n(n+1)(4n+5)

Now just use the results
Last edited by raheem94; 18-04-2012 at 23:22.
3. Re: FP1: Series homework help
Thank you for the reply, i have gotten to this stage and attempted to multiply out my answers.

I understand that 2\sum ^{n}_{r=1}r^2 is 1/3n(n+1)(2n+1), also that

\sum ^{n}_{r=1}r is 1/2n(n+1)

When multiplying out the brackets and such, i just can't seem to get the answer i need.
4. Re: FP1: Series homework help
(Original post by BigCal007)
Thank you for the reply, i have gotten to this stage and attempted to multiply out my answers.

I understand that 2\sum ^{n}_{r=1}r^2 is 1/3n(n+1)(2n+1), also that

\sum ^{n}_{r=1}r is 1/2n(n+1)

When multiplying out the brackets and such, i just can't seem to get the answer i need.

You don't need to multiply out all the brackets, just simplify the above expression.
5. Re: FP1: Series homework help
Remember to factorise as much as possible and don't expand. Makes it a lot easier and clear.
6. Re: FP1: Series homework help
I thank you both for your replies, although i still am struggling to manipulate the numbers to get the answer that i need, i'm very sorry.

I can't find a way to make: n(n+1)(1/3(2n+1)+1/2) = 1/6n(n+1)(4n+5)
7. Re: FP1: Series homework help
(Original post by raheem94)

You don't need to multiply out all the brackets, just simplify the above expression.
I thank you both for your replies, although i still am struggling to manipulate the numbers to get the answer that i need, i'm very sorry.

I can't find a way to make: n(n+1)(1/3(2n+1)+1/2) = 1/6n(n+1)(4n+5)
8. Re: FP1: Series homework help
(Original post by oli_G)
Remember to factorise as much as possible and don't expand. Makes it a lot easier and clear.
I thank you both for your replies, although i still am struggling to manipulate the numbers to get the answer that i need, i'm very sorry.

I can't find a way to make: n(n+1)(1/3(2n+1)+1/2) = 1/6n(n+1)(4n+5)
9. Re: FP1: Series homework help

Take n(n+1) out as a common factor now and simplify. You should get it

(Original post by BigCal007)
.)
Last edited by oli_G; 19-04-2012 at 01:18.
10. Re: FP1: Series homework help
(Original post by BigCal007)
I thank you both for your replies, although i still am struggling to manipulate the numbers to get the answer that i need, i'm very sorry.

I can't find a way to make: n(n+1)(1/3(2n+1)+1/2) = 1/6n(n+1)(4n+5)

Step 2: Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank

this is what you'll be called on TSR

2. this can't be left blank

never shared and never spammed

3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. By completing the slider below you agree to The Student Room's terms & conditions and site rules

2. Slide the button to the right to create your account

You don't slide that way? No problem.

Last updated: April 19, 2012
Study resources