Computing Upper & Lower Limit of {Sn} from Expression

[Ka Yan]

How can I compute the Upper and Lower limit of {Sn}, which defineded as: S1 = 0, S2m = S2m-1 /2, S2m+1 = 1/2 + S2m , directly from its expression, rather than by deduction of the terms?

(i.e., from the definition of Sn, instead of from 0, 0, 1/2, 1/4, 3/4, ...)

thks!

 

[tiny-tim]

Hi, Ka Yan!

Hint: deal with the even and odd terms separately.

That is, get an equation with only even terms in it, and another with only odd terms in it.

Instead of one series with two rules, that should give you two series each with only one rule, which is much easier!

 

[Ka Yan]

I got you!
That you mean, write S2m+1 = 1/2 + S2m-1 /2, and S2m+2 = (1/2 + S2m) /2 instead, isn't it?

Thank you!

 

[tiny-tim]

You're very welcome!

I assume you can finish it now, but if you can't after a few hours, come back for another hint!

[size=-2]ooh, you've worked out how to use "size"! [/size]​