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Hi, I was just wondering if anyone could help explain geometric series - I know that's not vey precise but it's the whole topic I don't really understand. I know that there's a thing called sum to infinity and I think there was something about n-1 (could be wrong?!) but I really just don't understand any of it!
GP's are sequences which have the first term named a and have a common ratio r
The next term is found by mutliplying the previous term by r
The formula for a GP is t(n)=ar^n-1
So for example the first term would = a
Second term = ar
Third term = ar^2 and so on...
When you want to find the sum of "n" number in the series you look at the value of r and see whether or not it is >1 or <1
When r<1 you use the formula Sum of GP = a(1-r^n)/1-r
And when r>1 you use Sum of GP = a(r^n-1)/r-1
It may look confusing but just look up some past papers and its just really all about subbing in values.
Summing to Infinity sounds hard but its really straightforward you just have to think logically.
When you sum to infinity "n" becomes an infinite size and for values -1<r<1 r^n would get closer and closer to zero (you are putting a decimal to a very high power thus it decreases)
so therefore 1-r^n could be rewritten as 1 and r^n would be so small
Due to this the summation formula changes and is
Sum to Infinity = a/1-r
for values of -1<r<1
They wont ask you to do a sum to infinity question where r lies outside these bounds.
Hope that helped.
Click on this link and then go to the website. I think that its really useful as there are notes as well as questions with answers.