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 ...
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, sum of n numbers is ...
$\\sum_{i=1}^n i$ 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 $\\sum_{i=1}^n i+(x-1)$.
How do I prove this by induction? Prove that for every natural number n, $ 2^0 + 2^1 + ... + 2^n = 2^{n+1}-1$ Here is my attempt. Base Case: let $ n = 0$ Then, $2^{0+1} - 1 = 1$ Which is true.
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 \times \f...
Possible Duplicate: How do I come up with a function to count a pyramid of apples? Proof that ∑ k=1n k2 = n(n+1)(2n+1) 6 ∑ k = 1 n k 2 = n (n + 1) (2 n + 1) 6? Finite Sum of Power? I know that the sum of the squares of the first n natural numbers is n(n+1)(2n+1) 6 n (n + 1) (2 n + 1) 6. I know how to prove it inductively. But how, presuming I have no idea about this formula, should I ...
Repeated sum is denoted using $\\sum$ and is called "summation." What is the name for the analogous process with multiplication, denoted $\\prod$?
