[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)

[raheem94]

(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

[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.

[raheem94]

(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.

[oli_G]

Remember to factorise as much as possible and don't expand. Makes it a lot easier and clear.

[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)

[BigCal007]

(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)

[BigCal007]

(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)

[oli_G]

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

(Original post by BigCal007)
.)

[raheem94]

(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)