How do I calculate this sum in terms of 'n'? I know this is a harmonic progression, but I can't find how to calculate the summation of it. Also, is it an expansion of any mathematical function? 1 ...

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 …

But is it possible to express the summation definition of $e^x$, without using them ? Since, I am regenerating my math knowledge I want to go step by step to calculus, differential equations …

Mar 30, 2015 · Explore related questions elementary-number-theory summation fibonacci-numbers See similar questions with these tags.

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Sep 2, 2017 · $\\sum_{i=1}^n i$ is the same as $\\frac{n(n+1)}{2}$. Can someone explain how the sigma notation is converted to this? I'm trying to figure out if there's a way to convert …

Explore related questions elementary-number-theory summation See similar questions with these tags.

Mar 3, 2018 · 13 $\displaystyle\sum_ {i,t}$ 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. …

How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression? For example here is the sum of $\cos$ series: $$\sum_ {k=0}^ {n-1}\cos (a+k \cdot d) =\frac {\sin (n …

Nov 17, 2017 · Explore related questions summation bernoulli-polynomials See similar questions with these tags.