MATLAB: Sum of geometric series without loop

geometricnarginseriestypingvararginwriting

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?

Best Answer

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!
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