1. ## 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

2. 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 $\displaystyle 0.00391+0.0352+0.00977+0.191$?

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

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

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

Then, for instance,

$\displaystyle f(1)=0.00391$

$\displaystyle f(2)=0.0352$

$\displaystyle f(3)=0.00977$

$\displaystyle f(4)=0.191$

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

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

So the summation is

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