Like what you saw?
Create FREE Account and:
 Watch all FREE content in 21 subjects(388 videos for 23 hours)
 FREE advice on how to get better grades at school from an expert
 Attend and watch FREE live webinar on useful topics
Geometric Series  Problem 2
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Summing a series, so behind me I have a series consisting of three terms and some dot, dot, dot which means that this is ongoing. So what this tells me is that I am summing a infinite series, there is no end, there is no specific sum this many terms. We don't have a formula for summing a infinite arithmetic sequence, so I'm hoping that this is a geometric series that I am dealing with.
So if geometric series we are going from one term to the next by multiplying by a consistent rate.
So what I see is some denominators for our second and third term but not our first, so I'm going to write in the denominator just to make my life a little bit easier to see if I can get any consistencies in this case. So I look at my denominators I'm going from 1 to 4 to 16 which tells me that I have to be multiplying by 4 in the denominator each time to go from one term to the next. So I know my rate is going to be something over 4.
Similarly I'm going from 5 to 15 to 45 in the numerator which tells me I'm multiplying by 3, but there is this sign change, I'm going from positive to negative and back to positive, the only way to do that is if we have a negative involved in there as well, so I know that my rate then has to be 3 over 4.
You can always check 5 times 3/4 is 15 over 4 times 3/4 is 45 over 16, so I found the rate for this geometric infinite series.
We now need to find the sum. We have a formula for the infinite sum; s is equal to a1 over 1 minus r, now all we have to do is plug in our information. We know that a1 is 5, that's easy enough and we know that our rate is 3/4 so this just becomes 1 minus 3/4. 1 minus 3/4 just becomes positive so this just becomes plus, so this becomes 5 over 1 plus 3/4, fourfourths plus 3/4 is just 7/4 dividing by a fraction just flip and multiply, so this is 5 times 4 over 7 which just leaves us with 20 over 7.
So finding a infinite sum, make sure it's a geometric series because in order for it to have an infinite sum, it has to be geometric, find your rate and then just plug it into your equation.
Please enter your name.
Are you sure you want to delete this comment?
Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
i love you you are the best, ive spent 3 hours trying to understand probability and this is making sense now finally”
BRIGHTSTORM IS A REVOLUTION !!!”
because of you i ve got a 100/100 in my test thanks”
Get Peer Support on User Forum
Peer helping is a great way to learn. Join your peers to ask & answer questions and share ideas.
Concept (1)
Sample Problems (14)
Need help with a problem?
Watch expert teachers solve similar problems.

Geometric Series
Problem 1 7,456 views1 + 1 + 3 + ... 6 2 2 Find S_{7} 
Geometric Series
Problem 2 6,138 viewsSum:
5 + 15 + 45 + ... 4 16 
Geometric Series
Problem 3 5,775 views_{7} ∑ 8(½)^{n} ^{i = 2} 
Geometric Series
Problem 4 739 views 
Geometric Series
Problem 5 620 views 
Geometric Series
Problem 6 717 views 
Geometric Series
Problem 7 643 views 
Geometric Series
Problem 8 606 views 
Geometric Series
Problem 9 618 views 
Geometric Series
Problem 10 618 views 
Geometric Series
Problem 11 614 views 
Geometric Series
Problem 12 540 views 
Geometric Series
Problem 13 642 views 
Geometric Series
Problem 14 633 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete