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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 …

Mar 8, 2015 · Proof is in the eye of the reader. A way I like to teach inductive proofs is to back up the inductive hypothesis by one, put the next item in it, then see if you match the claimed formula.

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 ...

What is the square of summation? Ask Question Asked 12 years, 3 months ago. Modified 1 year, 10 months ago.

$\begingroup$ 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 …

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

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 …

There are several things to remark here: First, $$\sum_{k=0}^{k=-2}\times 10$$ is not actually the correct notation.