Neither arithmetic nor geometric series problem

[Tayeeba]

Hello, I am trying to find a formula for this series, but isn't the last part seems like the formula? (-1)^(n-1) n^2
I am little but confused that what exactly the question is asking for?

 

[Deleted member 4993]

Hello, I am trying to find a formula for this series, but isn't the last part seems like the formula? (-1)^(n-1) n^2
I am little but confused that what exactly the question is asking for? View attachment 7654

This is your - problem you should know what is being asked for here!!

The question, I assume is asking you to calculate the sum.

Try grouping the following and factorize and let us know what you get:

(1² - 2²) + (3² - 4²) + (5² - 6²) + (7² - 8²)......

 

[Tayeeba]

This is your - problem you should know what is being asked for here!!

The question, I assume is asking you to calculate the sum.

Try grouping the following and factorize and let us know what you get:

(1² - 2²) + (3² - 4²) + (5² - 6²) + (7² - 8²)......

khan, thank you so much for the hint! It made the whole thing easier!!
So, I have come up with this, does it seem okay to you?

 

[Tayeeba]

...or (1^2 + 3^2 + 5^2....) - (2^2 + 4^2 + 6^2....)

but mine can be also right or no?

 

[Deleted member 4993]

khan, thank you so much for the hint! It made the whole thing easier!!
So, I have come up with this, does it seem okay to you? View attachment 7655

Yes and no.

Your summation is good.

But the nth. number of the new series is (A.P.) NOT the nth. number of the old series. Sp you need tobe extra careful about defining 'n'.

 

[Tayeeba]

Thanks guys ????