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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 …

$\begingroup$ 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 …

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

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 …

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 …

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.

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

Since you asked for an intuitive explanation consider a simple case of $1^2+2^2+3^2+4^2$ using a set of children's blocks to build a pyramid-like structure.