Finding the sum to n of 1/2^n

I'm trying to right a code which will output the sum of the series 1/2^n.

Ive used a for loop to iterate n from 1 to 20 for this example

My code keeps outputting 1/2^20 as the answer, instead of 1/2 + 1/2^2 + 1/2^3 ... +1/2^20

Here is my code

n = 0;

for n = 1:20

b = 1./(2.^n);

end

Sn = sum(b);

disp(Sn)

What am i doing wrong?

Answer 1

[Davide Masiello]

You haven't indexed the loop variable

for n = 1:20
    b(n) = 1./(2.^n);
end
Sn = sum(b);
disp(Sn)

    1.0000

You can also do it without loop

n = 1:20;
b = sum(1./(2.^n))

b = 1.0000

[Davide Masiello]

Of course, if you need the series to start from n=0, just replace n = 1:20 with n = 0:20. That also means you can't use n as loop iteration index, so you change to

n = 0:20;
for i = 1:length(n)
    b(i) = 1./(2.^n(i));
end
Sn = sum(b);
disp(Sn)

    2.0000

Answer 2

[Torsten]

format long
n = 1:20;
b = 1./2.^n;
Sn = sum(b)

Sn = 
   0.999999046325684