Help with sigma notation. The population of a local species of beetle can be found using an infinite geometric series where a1 = 960 and the common ratio is one fourth.

Question

britanyashton · Answer

Ok, you've given the information. What are they asking you to find out?

anonymous · Answer

960(1/(1-(1/4)))

anonymous · Answer

I need to write it in sigma notation and also try to find the sum. I dont know much about sigma notation at all, the giant E just confuses me

britanyashton · Answer

Oh ok. Well, thats simple. I'll teach you. It's not too confusing at all.

anonymous · Answer

Okay great, thank you so much

anonymous · Answer

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britanyashton · Answer

Tell me the formula for the sum of an infinite geometric series. You'll need that. We'll start there.

britanyashton · Answer

If you don't have your book open ill pull it up.

anonymous · Answer

I believe the equation is an=ar times r^n-1?

anonymous · Answer

so i would multiply 960 by 1/4 but what is n?

britanyashton · Answer

No. but you're close. It's the sum we're looking for, that formula only helps us find the value of one an in a series, rather than all of the values added up to a sum. 
the formula for this would be a=a1/(1-r)

britanyashton · Answer

I think thats where you got confused. :) You were using the wrong formula.

anonymous · Answer

oh okay, so it would be 960 / (1-1/4)?

anonymous · Answer

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britanyashton · Answer

Yes. If all information is placed right, then thats the sum! 
Does that make sense?

britanyashton · Answer

If so, we can get into sigma notation

anonymous · Answer

okay, that makes sense. But i have no idea what sigma notation is.

britanyashton · Answer

Don't worry. I'll give to you in English :P

britanyashton · Answer

That big E right there, is basically a symbol like a peace sign is a symbol for peace. xD But it translates: Between these numbers. 
remember a1, a2, ect... those are the numbers. The number on the top of the big E is where the series stops. It's the last term. You know that formula to the right of it? Plug in that top value into it, as the n, then you'll get the last value of the term. 
This is also true when you plug in your first term (the bottom value) into the formula on the right... you'll find the first term of the series. 

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