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Sum of n^2 summation formula question watch

1. Hi,

I just wanted to ask, how come these two summation formulas are the same? I can't visualise how the change in limits affect the signs in the formula

and

2. (Original post by ManLike007)
Hi,

I just wanted to ask, how come these two summation formulas are the same? I can't visualise how the change in limits affect the signs in the formula

and

Plugging 0 into gives 0 so the first sum is the same as

Then to get from

to

you just need to replace n by n-1. Does that help?
3. (Original post by Notnek)
Plugging 0 into gives 0 so the first sum is the same as

Then to get from

to

you just need to replace n by n-1. Does that help?
Ohhh okay, I see what you mean. Thanks!

But why does the sign change inside the brackets in the formula?
4. (Original post by ManLike007)
Ohhh okay, I see what you mean. Thanks!

But why does the sign change inside the brackets in the formula?
It depends what you mean by "why".

Can you see how if you replace the in the second expression with you end up with the first expression?

If you're looking for patterns and wondering why both signs in the brackets changed then this is just coincidental, or in other words this pattern won't always occur for similar questions.

E.g. if one of the brackets was then replacing by gives so this doesn't follow that "pattern".
5. (Original post by ManLike007)
Ohhh okay, I see what you mean. Thanks!

But why does the sign change inside the brackets in the formula?
Note the terms that correspond have changed position:
Attached Images

6. (Original post by Notnek)
If you're looking for patterns and wondering why both signs in the brackets changed then this is just coincidental, or in other words this pattern won't always occur for similar questions.

E.g. if one of the brackets was then replacing by gives so this doesn't follow that "pattern".
(Original post by ghostwalker)
x
Ah right, I can definitely see where you're coming from, that clears up my confusion!

Much appreciated for both of your contributions!

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Updated: February 9, 2018
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