Sum of the sum of harmonic series?

[Nikitin]

Homework Statement

Does this converge or diverge?

Ʃ1/(1+2+3+4+5...+n), as n---> infinity?

The Attempt at a Solution

I rewrote this into Ʃ(Ʃ1/n) (is it correct?).

I figured that since Ʃ(1/n) diverges, then the sum of each partial sum most (obviously) also diverge.

However, it appears I'm mistaken. Can somebody help?

 

[Ray Vickson]

Homework Statement

Does this converge or diverge?

Ʃ1/(1+2+3+4+5...+n), as n---> infinity?

The Attempt at a Solution

I rewrote this into Ʃ(Ʃ1/n) (is it correct?).

I figured that since Ʃ(1/n) diverges, then the sum of each partial sum most (obviously) also diverge.

However, it appears I'm mistaken. Can somebody help?

Is 1/(1+2) equal to (1/1) + (1/2)? Basically, you are claiming that the answer is yes.

RGV

 

[Nikitin]

oh crap. yeh you're right.

 

[hedipaldi]

1+2+...+n=n(n+1)/2,so compare with the convergent series 2/n(n+1)

 

[Nikitin]

ahh thanks. i completely forgot that you could rewrite 1+2+3..+n into n(n+1)/2.. thx!