Let N be a positive integer. Show that if a_n=b_n for n >= N, then Sum(a_n) and Sum(b_n) either both converge, or both diverge.

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Let N be a positive integer. Show that if a_n=b_n for n >= N, then Sum(a_n) and Sum(b_n) either both converge, or both diverge.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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@satellite73 can u help, plz?
what class is it?

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Other answers:

Cal 2
@Zarkon can u take a look at this too?
the sum up to N-1 is a finite sum so it doesn't contribute to the convergence or divergence of the series.
is assume \(\sum a_n\) converges then \[\sum_{k=1}^{\infty}b_n=\sum_{k=1}^{N-1}b_n+\sum_{k=N}^{\infty}b_n\] \[=\sum_{k=1}^{N-1}b_n+\sum_{k=N}^{\infty}a_n\] since \(\sum_{k=1}^{N-1}b_n\) is finite and \(\sum a_n\) converge...so does \(\sum b_n\)
tnx a lot man u're a lifesaver!
np

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