math - series help

[rocadelpunk]

link to problem

I was wondering if someone could give me a hint as to what direction/method i need to use to determine the sum.


We've only had like 2 lectures so far so not much has been covered, i dunno if i'm working ahead or not.

The teacher is a little nuts too and doesn't seem to be that great, at least compared to other math teachers I've had, anyways I won't blame him for anything, yet : P


From my understanding at this point, there's only a very few series you can even calculate the sums for:

I thought I'd try seperating the series into 3 smaller ones, so it'd be like sum from 1 to infinity of 4^n plus sum from 1 to infinity of 6^n minus one to infinity 11^n

but the r's for it aren't less then one so it'd just diverge...right? if i tried to do a geometric series

So i assume that doesn't work, the only other thing i can think of/read/understood is that this might be the Sn of a partial sum, but the only definition i have is infinite series k=1 to infinity of Ak converges and has sum S if the sequence of partial sums {Sn} converges to S...what's S?


help : (, can someone make some light of this for me? Thank you. If you have any good links that'd be sweet as well.

Brian.

 

[fawhfe]

Split it into 4^n/11^n=(4/11)^n and 6^n/11^n=(6/11)^n

 

[eigen]

Originally posted by: fawhfe
Split it into 4^n/11^n=(4/11)^n and 6^n/11^n=(6/11)^n

Bingo.

 

[rocadelpunk]

omg algebra : (


i'm embarrased : )

thanks.

 

[Tiamat]

believe it or not, its usually gonna be "oh its algebra" that bites you in the butt in lower level, and mid level math courses - Not the calculus or what-have-you.

 

[DrPizza]

I'll admit - that problem stopped me in my tracks for a moment or two. It's basically a challenging problem using the sum of an infinite series = a1/(1-4)

For anyone who didn't get it from above, it can be written as
Sum from n=1 to infinity of
(4/11)^n + (6/11)^n

or, expanded,

4/11 + (4/11)^2 + (4/11)^3 + ...
plus
6/11 + (6/11)^2 + (6/11)^3 + ...

The rest is easy.