Question

I need help with the zipper theorem proof.

Answer 1

what's the zipper theorem?

Answer 2

If series {a} and {b} go to L, then the series {c} consisting of osolating a, b members also goes to L. I don't know how to do subscripts on here, or I'd be more specific. It's second semester Calculus.

Answer 3

do you mean "sequence" or "series" ?

Answer 4

cause I don't think that's true for series, only sequences

Answer 5

begin by assuming the definition of convergence for each series \(\{a_n\},\{b_n\}\) and state those definition formally. \[\{a_n\}\to L\iff\exists N|\forall n>N,~~|a_n-L|<\epsilon\]

Answer 6

so you understand that definition and notation?

Answer 7

Omg, yes! Sequences! Series was last chapter. My bad.

Answer 8

do*

Answer 9

Yes. How do I go from there?

Answer 10

write the same definition for the sequence \(\{b_n\}\) using some other index, \(M\)
in a sequence that consists of the elements a1, b1, a2, b2, ... you can then show that if you rename the indices of this sequence and write
\(\{c_n\}=c_1,c_2,c_3,...\) you can figure out the index at which the same definition holds (hint: it can be written in terms of M and N; think of how the Nth term and Mth term relate to the new sequence))

Answer 11

if you need further help let me know

Answer 12

Thank you very much!