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

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Richard Ledford 2022-1-30

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https://ww2.mathworks.cn/matlabcentral/answers/1638955-using-summation-and-series-to-create-a-function-to-analyse-and-find-error

回答： Binaya 2023-10-19

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.

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Answer 1

Binaya 2023-10-19

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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:

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