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 ...

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

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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) …

Mar 8, 2015 · 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 = …

Jul 4, 2023 · I was just recently introduced to Big-O notation and this confused me. When summing from 1 to n, why is the time complexity O(n2)? In other words, why is $\\sum_{i=1}^n …

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 …

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

Feb 25, 2015 · Rules for Product and Summation Notation Ask Question Asked 12 years, 1 month ago Modified 6 years, 2 months ago

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 …