Trick Of The Day (Alex) - Infinite Sequences

Ok, it's time for my shot at the trick of the day.

NOTE: This only works on geometric sequences (same multiplication factor throughout)

Infinite sequences... pretty simple really.
The formula goes like this. (first term of the sequence) / (1 - (multiplication factor))

Examples:
1.
3, 1.5, .75 ...
You need to multiply by 1/2 to get the next term, so the formula looks something like this.
3 / (1 - .5)
3 / .5
Answer : 6

I'll show a couple more examples... you can probably figure the multiplication factors out for yourselves.
2.
1, .8, .64 ...
Answer : 5


3.
5, 2, .4 ...
Answer : 25/3

You should note that the above formula only works on geometric series. If you get some other type of series (Fibonacci, arithmetic, etc.), you need a different method.

Oh, right, thanks.
By the way, i haven't talked to you in a while havern. How's it going?

Not bad, I suppose. How are you?

Decent, bee doing pretty bad in contest though.

While we're on the series topic, can someone please post a way to find the sum of an arithmetic sequence easily?

you mean such as 2 + 4 + 6 .... + 22?

Alex Tatge wrote:you mean such as 2 + 4 + 6 .... + 22?

nvm, its in the uber file I'm about to post once Michael tells me how to upload files =(
wait, send me ur email, and I'll mail you the uber trick folder.

its alex.tatge@gmail.com

I posted the rapidshare link on the page for the folder, please tell me if it works.