How to apply the sum function of a factorial equation without using the factorial function

How do I use SUM and nested FOR loops to calculate the sigma notation of (2^i)/(i!) when i=0..20 without using the function factorial(i)?

I've tried

A=2^i

SUM(A)=0

for i=1:20

SUM(A)=SUM(A)+i

but this already doesn't work, and I cannot add the nested for loop of the factorial until I have this. How would this nested for loop look without using the factorial() function?

Answer 1

[sixwwwwww]

Dear Anj, do you need something like this:

i = 1:20;
val = sum(2.^i);

[Anj]

Yes, I've gotten this far but I need to use a FOR Loop to divide each of these values by i! without using the factorial() function on matlab.

In other words SIGMA[(2^i)/(i!)] when i goes from 1 to 20.

[sixwwwwww]

you need this:

2^i / i!

in each loop iteration? and then sum up all values?

[Anj]

Yes, but without explicitly using the factorial() function.

[sixwwwwww]

ok. let me check it

[sixwwwwww]

Here is the code:

sum_all = 0;
for i = 1:20
    power_val = 2^i;
    fact = 1;
    for j = 1:i
        fact = fact * j;
    end
    sum_all = sum_all + power_val / fact;
end
disp(sum_all)

[Anj]

It works. Thank you!

[sixwwwwww]

you are welcome

[Image Analyst]

Your inner for loop can be replaced simply by

fact = prod(1:i);

Also we recommend using k or some other variable than i (the imaginary variable) for a loop counter (though it will work). So then your entire program above (now hidden) becomes simply:

sum_all = 0;
for k = 1:20
    sum_all = sum_all + 2^k / prod(1:k);
end
disp(sum_all)

[sixwwwwww]

Yes you are right. But I used nested for loop because it was insisted by Anj to use nested for loop. Thanks for suggestions about 'i' as loop variable. I will try to avoid it although it is my habit to use 'i' as loop variable. Thanks a lot nevertheless

[Image Analyst]

You're right. I don't know why teachers have students ignore the best part of MATLAB (vectorization) when that is exactly the perfect opportunity to demonstrate it.