Sum of geometric series without loop
13 views (last 30 days)
Show older comments
Kenan Hoyt
on 20 Jun 2014
Commented: Roger Stafford
on 21 Jun 2014
Hey! For the function geo(r,varargin) i am trying to find the sum of the following
1 + r + r^2 + r^3 + r^4 + ... + r^n
where n = nargin.
I have searched and lurked at every corner both here and in the "help" in Matlab, but i found no way of "writing"/"setting up" the geometric series without loops, which is what i am trying to accomplish. Finding the sum i can do, but i cannot find a way to write above series without too much effort. Any ideas? What obvious built-in function am i missing?
0 Comments
Accepted Answer
Geoff Hayes
on 20 Jun 2014
I'm not all that clear on why you are using n=nargin instead of just passing n into the function as the second input but maybe there is more to your function than just the series.
You can try using cumprod which returns the cumulative product of each element in the input array. For example,
cumprod([1 2 3 4 5])
returns
1 2 6 24 120
where each element (starting from second) is multiplied by the previous element. You can do something similar with r and n as follows
% create a vector with n elements all identical to r
v = r*ones(1,n);
% calculate [r r^2 r^3….r^n]
v = cumprod(v);
% sum and add one
geoSum = 1 + sum(v);
Try the above and see what happens!
More Answers (1)
Roger Stafford
on 20 Jun 2014
A simpler method:
result = (1-r^(n+1))/(1-r);
2 Comments
Roger Stafford
on 21 Jun 2014
It is easy to see why this works. Call the sum s:
s = 1 + r + r^2 + r^3 + r^4 + ... + r^n
Then
s*r = r + r^2 + r^3 + r^4 + r^5 + ... + r^(n+1)
Therefore when you subtract s*r from s, all the terms cancel except the first and last ones:
s - s*r = 1 - r^(n+1)
Hence if you divide both sides by 1-r you get
s = (1-r^(n+1))/(1-r)
See Also
Categories
Find more on Loops and Conditional Statements in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!