I seem to be missing something.

[Loki123]

I have suggested answers, I have written them on the paper. The area of three squares did not match the answer so I added more because I thought "etc." in the question meant I had to add more (to what extent, Idk.) I didn't get a correct answer. Why is that?

 

[R.M.]

Are you trying to derive a sum of the areas? To me it's not entirely clear what the problem is asking you to do. If you're trying to create a sum of areas, take your formula for the first three squares and factor out an a². Does that series look familiar?

 

[Loki123]

In your sum of the first three squares, factor out an a². Does that series look familiar?

7/4? not really

 

[Loki123]

7/4? not really

oh wait it does, a geometric series

 

[R.M.]

a²(1 + 1/2 + 1/4). If you do the same with your first 5 terms: a²(1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32). What kind of series is this?

 

[Loki123]

a²(1 + 1/2 + 1/4). If you do the same with your first 5 terms: a²(1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32). What kind of series is this?

Is this right

 

[R.M.]

Is this right
View attachment 32532

Bingo.

 

[Loki123]

Bingo.

thank you so much ♥