Question

I'm having trouble understanding part of my textbook (Calculus II, section on convergent and divergent series and sequences), could somebody explain this to me? (Part in question posted below in a minute).

Answer 1

I'm not understanding why the terms of the series form a sequence that converges to zero. I don't understand that.

Answer 2

(I get that the general term of that sequence, if you take the limit of it as n approaches infinity, it will be zero, but that's not the same, right?)

Answer 3

yes

Answer 4

"yes" what.

Answer 5

its goes to 0 as we let n get large, thus it converges to 0

Answer 6

it goes*

Answer 7

But the series itself doesn't, correct?

Answer 8

correct

Answer 9

I'm just a little offset by the wording of, "However, the terms of the series...", both plural, and "series" is used, it's implying a sum and multiple terms, converge to zero. The nth term converges, but the series doesn't. Egh, it's just bad writing. Thanks.

Answer 10

the sequence converges
the series does not

Answer 11

word np

Answer 12

Thanks.