summation; See similar questions with these tags. Featured on Meta Changes to reporting for the [status ...

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 …

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 ...

summation; Share. Cite. Follow edited Feb 12, 2023 at 22:45. mjc. 2,331 10 10 silver badges 19 19 bronze ...

$\begingroup$ It must be mentioned here why the interchange of summation and differentiation is justified. It is justified by the fact that convergent power series converge uniformly on compact …

Jun 22, 2023 · Notation for Multiple summation. 57. How to change the order of summation? 0.

Mar 3, 2018 · $\displaystyle\sum_{i,t}$ means the same as $\displaystyle\sum_i \sum_t$. In the second notation, a specific summation order is given, whereas in the first one there isn't. So …

Nov 18, 2016 · summation; permutations; See similar questions with these tags. Featured on Meta Changes to reporting for ...