Simplify this equation?

[ViRaLRuSh]

1^2 + 2^2 + 3^2 ......n^2

What could it be? is it (n+1)^2? Just wondering cause I know it's gonna be on my Data Structures final

 

[AvesPKS]

Well, it's a series...so, it'd be a sigma in front, with n=1 on the bottom, n=infinity at the top, and n^2 to the right of the sigma...right?

 

[ViRaLRuSh]

ahhh yes, sounds about right. Thanks!

∞
Σ n²
n=1

 

[gopunk]

(N(N+1)(2N+1))/6

 

[pillage2001]

Originally posted by: gopunk
(N(N+1)(2N+1))/6

?????

 

[ViRaLRuSh]

He's right, that is the technically right equation for what I posted above.

 

[Orsorum]

Originally posted by: pillage2001

Originally posted by: gopunk
(N(N+1)(2N+1))/6

?????

That's the solution to the summation.

 

[oboeguy]

Sounds right. Note that there's no "infinity" in the first post, it simply goes to "n". So the summation notation form should not use "n" as the index, tsk tsk. 😀

 

[pillage2001]

Originally posted by: Zakath15

Originally posted by: pillage2001

Originally posted by: gopunk
(N(N+1)(2N+1))/6

?????

That's the solution to the summation.

LOL, I did not bother to expand the calculations. 😀

 

[gopunk]

yups

and for a data structures class, you should probably note that an algorithm with that order time complexity is O(n^3)

 

[ThaGrandCow]

42.

 

[ViRaLRuSh]

Originally posted by: gopunk
yups

and for a data structures class, you should probably note that an algorithm with that order time complexity is O(n^3)

Man, you're some sort of wiz-kid 🙂

p.s. I hate complexities

 

[AvesPKS]

Originally posted by: oboeguy
Sounds right. Note that there's no "infinity" in the first post, it simply goes to "n". So the summation notation form should not use "n" as the index, tsk tsk. 😀

Damn...I've been up for 26 hours writing a polisci paper due at...45 minutes...

 

[Dacalo]

Originally posted by: AvesPKS

Originally posted by: oboeguy
Sounds right. Note that there's no "infinity" in the first post, it simply goes to "n". So the summation notation form should not use "n" as the index, tsk tsk. 😀

Damn...I've been up for 26 hours writing a polisci paper due at...45 minutes...

lol been there 😛

 

[DrPizza]

And, just in case you should ask,

1^3 + 2^3 +3^3 +4^4 + ... + n^3 = (n^2)(n + 1)^2/4

(want the 4th, 5th, 6th too?)