Calculate a Sum Product

Calculator for sum products, a product Π of sums Σ. The inner sum with the running variable j runs from o to p, the outer product with the running variable i runs from m to n. Only the variables i and j may occur in the sum term. The basic arithmetic operations + - * / are allowed, as well as the power function, like pow(j#i) for jⁱ. Further allowed functions are sin(), cos(), tan(), asin(), acos(), atan(), log() for the natural logarithm and fac() for the factorial. Also, the constants e and pi can be used. If i≠j is chosen, factors with equal running variables are omitted. The double product can quickly lead to very high values.

Outer product from m= to n=

Inner sum from o= to p=

Show each step in a table Only show end result i≠j

Round to 0 1 2 3 4 5 6 7 8 9 10 11 12 13 decimal places.

Using the preset values, a simple sum product is calculated. At each step, the sum of the two counter variables i and j is calculated. These sums are 2, 3, 4, 5, and 6 in the first row. These initial five individual sums, corresponding to the number of steps for j, are added step by step. This yields the first intermediate result, which in this case is 20. The process then continues with the next five individual sums, 3, 4, 5, 6, and 7, which are then added together to obtain the next intermediate result, here 25. The two intermediate results are multiplied by each other to get 500. This is done only once again, because the number of steps for i is three. The third intermediate result is 30, and the product of all intermediate results, and thus the final result in this example calculation, is 15000.

Besides the sum product, there is also the product sum, where the calculation is reversed. There, the inner products are added together. Both calculators use the same example values, allowing for a good comparison of the behavior of the sum product and the product sum. It is impossible to say definitively which method leads to faster increasing or converging results. This depends on the values ​​used and the number of individual additions and multiplications. For the given example values, the product sum is higher up to the second row, after which the sum product surpasses it.