# Extremely Urgent!

• Jan 6th 2008, 07:55 AM
samantha_malone
Extremely Urgent!
I have four values, and I have to put them in summation notation. It would be appreciated if someone could help me, thanks!

0.00391
0.0352
0.00977
0.191

I guess it would help converting them into fractions at first, but I don't seem to know where to move on from there because I can't seem to find a pattern between the four values. Your help would greatly be appreciated.

Thanks,
Sam
• Jan 6th 2008, 01:03 PM
DivideBy0
Quote:

Originally Posted by samantha_malone
I have four values, and I have to put them in summation notation. It would be appreciated if someone could help me, thanks!

0.00391
0.0352
0.00977
0.191

I guess it would help converting them into fractions at first, but I don't seem to know where to move on from there because I can't seem to find a pattern between the four values. Your help would greatly be appreciated.

Thanks,
Sam

Hi samantha,

Do you mean $0.00391+0.0352+0.00977+0.191$?

I think there are many ways you could do this, but the easy way out is to use a cubic polynomial, i.e.

$\sum_{x=1}^4 (ax^3+bx^2+cx+d)$

Why? Because we have four values, we can create four equations, and since a cubic polynomial has four unknowns, we can solve for them, integrating our values into the sum... it's hard to explain, but easier if we just do it!

Let $f(x)=ax^3+bx^2+cx+d$

Then, for instance,

$f(1)=0.00391$

$f(2)=0.0352$

$f(3)=0.00977$

$f(4)=0.191$

Solving either using a calculator or by hand (:eek:), we get

$(a,b,c,d)=\left(\frac{13169}{300000}, -\frac{14587}{50000}, \frac{17977}{30000}, -\frac{8687}{25000}\right)$

So the summation is

$\sum_{x=1}^4 \left(\frac{13169}{300000}x^3-\frac{14587}{50000}x^2+\frac{17977}{30000}x-\frac{8687}{25000}\right)$