Using summation and series to create a function to analyse and find error

I have a series of 10^(N-1) minus a summation of k=1 to 10^(N) of 0.1. I havn't worked with sums and series in a while and was wondering how to get exact value of N and what ever information you could give on composing the function with a for loop. I think that might help me figure out the function I need to create in my project. I have seen a lot of information on summations and how to put into a script in matlab, but I have found nothing on how I can do this with a power of N on the upper limit. Thankyou in advance. Any information you can provide would be helpful. P.S. Yes, I have looked up how to do summations in matlab and have not yet found how to do this particular problem. I know I need to use a for loop.

Answer 1

[Binaya]

Hi Richard,

Based on your description, you would like to develop a MATLAB code using for loop for the series “10^(N-1)” and a summation of “k=1 to 10^(N)” of “0.1”, and take its difference.

Please find the below algorithm as a possible solution to your query:

1. Initialize “sum1” and “sum2” as 0
2. Initialize a value of “N”
3. Start a for loop from 1 to “N”
4. Update sum1 by incrementing it with “10^(k-1)”
5. After the for loop, update “sum2” as “0.1*10^N” as using for loop here would increase the time complexity exponentially.
6. Finally take the difference of “sum1” and “sum2”.

Please refer to the below Mathworks documentation for more reference:

1. For loop: https://www.mathworks.com/help/matlab/ref/for.html

I hope this helps.

Regards 

Binaya