Direct expression for sum of squares

cscott
Messages
778
Reaction score
1
How do you go from \sum_{n = 1}^n i^2 to \frac{n(n + 1)(2n + 1)}{6}?
 
Physics news on Phys.org
Prove the formula by induction.
 
I think you forgot to include something, what you wrote should simplify to n i^2.

Edit: Unless I'm missing something :confused:
 
Oops, the index should be i, not n as you've written.
 
Thanks for the info.

My mistake with the index.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

On pointwise convergence of Fourier series
Replies
3
Views
2K
How to show that these sequences are summable?
Replies
1
Views
1K
Proving that ##\lim [\sqrt{4n^2 +n} - 2n] = \frac{1}{4}##
Replies
9
Views
3K
##\lim_{n\to\infty}\left(n\left(1+\frac1n\right)^n-ne\right)=?##
Replies
5
Views
2K
Solve the problem involving sum of a series
Replies
2
Views
1K
Fourier series of this scale and shift of triangle wave
Replies
1
Views
1K
Calculating area using sigma notation
Replies
8
Views
2K
Proving convergence of rational sequence
Replies
2
Views
1K
Induction with binomial coefficient
Replies
15
Views
2K
Expressing a limit as a definite integral
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top