Solve Converging Sequence: 1 + 1/8 + 1/27 + 1/64...

[Hockeystar]

Homework Statement

Solve 1 + 1/8 + 1/27 + 1/64...

Homework Equations

Stuck here.

The Attempt at a Solution

I know the series is infinitetly adding 1/n^3. I know it should converge. How do I solve as lim x--> infinity. Teacher never gave us any info, he just said use number sense.

 

[Mark44]

Homework Statement

Solve 1 + 1/8 + 1/27 + 1/64...

Homework Equations

Stuck here.

The Attempt at a Solution

I know the series is infinitetly adding 1/n^3. I know it should converge. How do I solve as lim x--> infinity. Teacher never gave us any info, he just said use number sense.

What exactly does "solve" mean? Are you supposed to find the sum of this series, or do you only need to say that it converges or diverges?

If it's the latter, do you know any tests you can use to determine convergence or divergence?

 

[payumooli]

try integral test

 

[Hockeystar]

My teacher wanted to know the sum. Integral test is as n--> infinity, 1/x^6 is finite (0). Therefore the series converges. How do I find the sum then? Sohuld I just try trial and error and see what it seems to approach?

 

[Bohrok]

I don't think there's a good closed form for that sum other than ζ(3), the Riemann zeta function.

 

[Hockeystar]

I could do 1/n^2 infinite sum is (pi^2)/6 and then multiply by infinite 1/n but that series diverges. Found solution on wikipedia. http://en.wikipedia.org/wiki/Apéry's_constant

I think my teacher was just looking for a decimal approx (only H.S calc. class) Thanks for the help everyone.