One more proof question. malevolence19 if you could be so kind.

Question

anonymous · Answer

attachment

anonymous · Answer

any thoughts?

anonymous · Answer

This one is a bit tougher haha

anonymous · Answer

yea its a fun class let me tell you

anonymous · Answer

I honestly don't know too much about sums of subsequences being convergent being related to absolute convergence of a series :/

anonymous · Answer

Lets think about it outloud

anonymous · Answer

Im wondering if i have to prove if i prove that bn is a cauchy sequence

anonymous · Answer

For b_n to be a subsequence of a_n then it must have the property that:
$$b_k=\left\{ a_{n_k}| n_1 < n_2 < ... < n_k \in \mathbb{Z}^+\right\}$$

anonymous · Answer

Maybe I'm going too basic D:

anonymous · Answer

Im not sure. He posted this friday and we have a week to get it done so there is a possibility he hasnt covered it in class yet

anonymous · Answer

Do you know abel's test?

kinggeorge · Answer

Could you say that $a_n$ is a subsequence of itself? Thus it's convergent. You still need to show absolute convergence, but this might be a good first step if it works.

anonymous · Answer

I mean we did just talk about rearrangement of series

kinggeorge · Answer

Absolute convergence would follow from the fact that $$\sum_{n=1}^{\infty} a_n$$converges. Since it converges at infinity, it's absolutely convergent.

kinggeorge · Answer

Just found this, it might help. http://www.physicsforums.com/showthread.php?t=209040

anonymous · Answer

it does. thanks

kinggeorge · Answer

you're welcome