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 …

Explore related questions summation exponential-function See similar questions with these tags.

Feb 10, 2019 · We have the sum $$\\sum_{k=0}^{n} a^k k,$$ where a is a constant and we need the answer in terms of $n$. How can we go about solving this? If $a$ were a variable we ...

What are the (most important) rules of double sums? Below are some rules I encountered - are they all correct and complete? Offerings of clear intuition or proofs (or other additions) are …

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 …

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 …

Apr 19, 2015 · I would like to know if there is formula to calculate sum of series of square roots 1√ + 2√ +⋯+ n√ 1 + 2 + + n like the one for the series 1+2+…+n= n(n+1) 2 1 + 2 + + n = n (n + 1) …

What is interesting is that your formula is the closed form for a different summation, i.e. $\displaystyle \sum_ {i=0}^n \binom {i+1}2=\sum_ {i=0}^n \frac {i (i+1)}2=\frac {n (n+1) …

Oct 2, 2016 · Question: Is it possible to show this, purely by manipulating the summand, and without first expressing the summation in closed form and then factoring the sum of squares?