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# Stuck on AS Further Maths Series Question! watch

1. I wrote the series as an expression first which gave me:

n(n+1)(2n+1)/2 - n(n+1) -1

I then simplified this expression to n(n+1)(2n-1)/2 - 1.

I'm unsure on what steps I need to take to get to the answer, which is:
n(2n+3)(n-1)/2

See question below:
Any help would be appreciated!
2. Question:
Attached Images

3. (Original post by dotoswift)
Question:
That's not entirely correct.

Note that

Now note the last sum - it is not 1
4. (Original post by RDKGames)
That's not entirely correct.

Note that

Now note the last sum - it is not 1

Is this the first step then? :

n(n+1)(2n+1)/2 -n(n+1) - (3-2-1)
5. (Original post by dotoswift)
Is this the first step then? :

n(n+1)(2n+1)/2 -n(n+1) - (3-2-1)
Why? Where did 3-2-1 come from? Try to justify every move you make otherwise you end up writing rubbish without a reason.

The first two expressions are correct, so don't try to change those.

Summing up 1 an number of times means a total of times. Hence what is ?
6. (Original post by RDKGames)
Why? Where did 3-2-1 come from? Try to justify every move you make otherwise you end up writing rubbish without a reason.

The first two expressions are correct, so don't try to change those.

Summing up 1 an number of times means a total of times. Hence what is ?
It is 1n.
7. (Original post by dotoswift)
It is 1n.
Yes, so then proceed with that correction. Factor out and simplify the bracket.
8. (Original post by RDKGames)
Yes, so then proceed with that correction. Factor out and simplify the bracket.
Thanks so much for your help.

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