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5 Answers. Changing the order in the first double sum is manageable. We could therefore use it as some kind of prototype. We transform the second double sum, so that the index range is similar to the first one.
Then the product of sums is the area of the entire rectangle, whereas the sum of products is only the red area. So the original summation is definitely not the same as this double sum. To answer your question specifically, you should not split this into two different summations.
To answer your question specifically, you should not split this into two different summations. Rather, notice that P does not depend on k. You can treat P as a constant and simply move it outside the summation so that it multiplies the result of your summation of OK, which does depend on your variable k.
Splitting summations One way to obtain bounds on a difficult summation is to express the series as the sum of two or more series by partitioning the range of the index and then to bound each of the resulting series.
Similarly, you can break a sum inside a series into the sum of two separate series: For example: A little algebra allows you to split this fraction into two terms: As with the Sum Rule for integration, expressing a series as a sum of two simpler series tends to make problem-solving easier.
1:38 7:32 Suggested clip Summation Formulas and Sigma Notation (Part 4) Examples YouTubeStart of suggested client of suggested clip Summation Formulas and Sigma Notation (Part 4) Examples
2 Answers. It is not correct to divide. If it is useful, you might rewrite as I=0ni(bi1)0(modb1).
Splitting summations One way to obtain bounds on a difficult summation is to express the series as the sum of two or more series by partitioning the range of the index and then to bound each of the resulting series.

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