Not true. Consider the alternating series,

1-1/3+1/2-1/3[sup]2[/sup]+1/3-1/3[sup]3[/sup]+1/4-1/3[sup]4[/sup]+1/5-1/3[sup]5[/sup]+............

diverges but terms approach zero.

The correct statement is "all alternating series where the terms approach zero and absolute values of the terms decrease converge"

Gaja

 

Good point. Althouth it should read, ". . . absolute values of the terms eventually decrease . . ."; what happens with the first n terms (n any whole number) is irrelevant.

 

Again, good point.

I haven't looked at infinite series for a while; now that you mention the sum, it's obvious.

 

If the infinite sum is equal to e^(-1/2)

Then we have
{e^(-1/2)^4B}
which = e^(-2B)

collecting like terms we have
e^0
which = 1

Which leaves me with
[{alpha^2/(alpha*beta^2)} + 1]

I'm so lost... how did you get rid of the alphas and betas???

 

I don't see any alpha in the original. Where'd you get them?

 

Looks like greek alphabets aren't my forte either lol. What does that symbol that looks like a mirrored "6" represent then? Is it just a variable?

 

It designates a partial derivative: for a function of more than one variable it is the derivative with respect to one of the variables, treating the other variables as constants.

It's out of place here because the function e[sup]53β[/sup] has only one variable: β; it would be more appropriate to have d[sup]2[/sup]/dβ[sup]2[/sup]: the second derivative with respect to β.

 

thanks magician =)

 

So my final answer is 416 - [625 - 37] - [2810]
= 416 - 588 - 2810
= -2982


does that look right?

 

My pleasure.