while loop to count partail sum of series

Hello,

I'm having problems making while loop to count partial sum (110 iterations) of this series: 1/i*(i+1). There is antoher condition that counting precision must be 1e-4. So the loops breaks when all iterations are done or the precision is achieved. Unfotunetely I'm new to MATLAB and haven't ever done series using while only using for.

Here's what I managed to do, as you can see I haven't done antyhing regarding precision since I don't how to do it and the loop is infinite becasue I don't know to make a proper condiiton to break.

i=1; N=110; x=0;
while 1
    x1=1/(i*(i+1));
    x=x+x1
    if i>=N
        break
    end
end
disp(x)

Answer 1

[Image Analyst]

Two problems.

1. You forgot to increment your loop counter, the (badly-named) i.
2. You forgot to index x so you're just overwriting it every time.

The fix:

N = 110; % Max iterations.
x = zeros(1, N);
x(1) = 1 / (1 * 2);
loopCounter = 2;
while loopCounter <= N
    thisTerm = 1 / (loopCounter * (loopCounter+1));
    x(loopCounter) = x(loopCounter - 1) + thisTerm;
    loopCounter = loopCounter + 1;
end
plot(x, 'b-', 'LineWidth', 2);
grid on;
xlabel('Iteration Number')
ylabel('x, partial sum')

[Torsten]

x(1) = 1 / (1 * 2);

instead of

x(1) = 1 / (1 + 2);

And

x = zeros(1, N);

must be done before setting

x(1) = 1 / (1 * 2);

[Image Analyst]

Thanks @Torsten for catching those problems. 🙂 I've corrected them in my initial answer.

Answer 2

[Torsten]

sum_{i=1}^{i=N} 1/(i*(i+1)) = 1 - 1/(N+1)

No need for such a difficult while construction with precision estimate.

[Arkadius882]

The problem is that it needs to be with while loop because that is an academic task :/

[Torsten]

Then use Image Analyst's solution.