Do Merged Mathematical Sequences Converge to the Same Limit?

[sedaw]

thres two series An and Bn , Bn unite with An from some index.

need to prove that limAn_k = limBn_m

Bn_m and An_m are sub series .

TNX !

 

[diegzumillo]

Hi there,
I don't really understand your question. Could you detail it a little more? What exactly is this limit? And what do you mean by "unite with"?

 

[HallsofIvy]

Do you mean alternate sequences so we have $a_n, b_n, a_{n+1}, b_{n+1}, ...$ from some n? In any case, you can't prove what you say- {a_n} and {b_n} could be two independent sequences with completely different limits.

What you can prove (assuming that is what you mean by "unite") is that the "united" sequence converges if and only if {a_n} and {b_n} converge to the same thing.