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 ...

Easy way of memorizing or quickly deriving summation formulas Ask Question Asked 10 years, 2 months ago Modified 5 years, 1 month ago

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

What is interesting is that your formula is the closed form for a different summation, i.e. $\displaystyle \sum_ {i=0}^n \binom {i+1}2=\sum_ {i=0}^n \frac {i (i+1)}2=\frac {n (n+1) (n+2)}6=\binom {n+2}3$.

The first chapter of Concrete Mathematics by Graham, Knuth, and Patashnik presents about seven different techniques for deriving this identity, so you might be interested to look at that.

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 example, …

Jan 18, 2026 · So I was reading example 5.9 in Evan Chen's "Summations" handout (pdf link via evanchen.cc), and I wondered: How would anyone ever calculate $$\\sum_{k=0}^\\infty\\limits …

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 …

How do you write the summation of a summation? Ask Question Asked 13 years, 3 months ago Modified 13 years, 3 months ago

Apr 3, 2021 · Repeated sum is denoted using $\\sum$ and is called "summation." What is the name for the analogous process with multiplication, denoted $\\prod$?