How to create a function to find the sum of a geometric series?

I want to create a function to find the sum of a geometric series and the number of terms is defined by n. I'm new to MATLAB so I haven't worked with this program a lot. My initial idea going in would be to create a loop depending on the variable n and find the sum for the values.

[Sebastian]

Geoff Hayes already provided an answer to this question, see https://de.mathworks.com/matlabcentral/answers/136667-sum-of-geometric-series-without-loop

[SHUBHAM PHOOLARI]

Let's make it simple for you

function s = gseriessum(r,n)

 %function to calculate sum of geometric series

nvector = 1:n ; %create a vector from 1 to n

gseries = 1+r.^nvector ; %create vector of terms in series

s = sum(gseries);

%run the function gseriessum(r,n) on the command window with your inputs for 'r' and 'n'

Answer 1

[Walter Roberson]

Let the first term of the geometric series be C, and let each one after that be f times greater than the one before. So C, (C)*f = C*f, (C*f)*f = C*f^2, (C*f^2)*f = C*f^3 and so on. Then the K'th term is C*f^(K-1) if you number starting from 1, and you have

syms C f K N
simplify(symsum(C*f^(K-1),K,1,N))

There is an important geometric series identity that will get used here, giving the result

C*(f^N-1)/(f-1)

Now you can just substitute in the initial term and the multiple per term and the number of terms.

[Adam Wanliss]

How can I do this without the symbolic math toolbox? I don't have access to syms

[Walter Roberson]

result = C*(f^N-1)/(f-1) where C is the initial value, f is the multiple for the terms, and N is the number of terms.