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I would use a matrix-notation. I assume your original values are in a vector S, say $ S=[a,b,c,d] $ and then I'd express the transformation to the vector Q using the triangular matrix D with

Oct 29, 2016 · I know that the sum of powers of $2$ is $2^{n+1}-1$, and I know the mathematical induction proof. But does anyone know how $2^{n+1}-1$ comes up in the first place. For …

Then the bracket itself is differentiated, producing the 2 at the front. The 2nd step on line 1 involves no differentiation. Instead, the bracket is split into two terms. The second term has an …

Assuming that the former interpretation was meant (double summation) it would be much better to write it as $$ \sum_{j=1}^N \sum_{i<j} d_{i,j}, $$ which makes the double summation obvious; …

May 31, 2017 · The scope of the series operator is the following term; it encompassed any multiplication (or division). $$\sum_i \color{blue}{x_iy^i} = \sum_i \color{blue}{y^ix_i}$$

Dec 11, 2014 · When we deal with summation notation, there are some useful computational shortcuts, e.g.: $$\\sum\\limits_{i=1}^{n} (2 + 3i) = \\sum\\limits_{i=1}^{n} 2 + \\sum ...

Aug 27, 2013 · Where, i represents the index of summation; a_i is an indexed variable representing each successive term in the series; m is the lower bound of summation, and n is …

What is the square of summation? Ask Question Asked 12 years, 3 months ago. Modified 1 year, 9 months ago.

Nov 29, 2014 · To put this in context, I am wondering if there is a formula that one can use for the summation of trig functions. There are formulas for summation of polynomials. i.e $$ …