## bahrom7893 3 years ago 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.

1. bahrom7893

@satellite73 can u help, plz?

2. bahrom7893

@imranmeah91 ?

3. imranmeah91

what class is it?

4. bahrom7893

Cal 2

5. bahrom7893

@Zarkon can u take a look at this too?

6. Zarkon

the sum up to N-1 is a finite sum so it doesn't contribute to the convergence or divergence of the series.

7. Zarkon

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 $$\sum b_n$$

8. bahrom7893

tnx a lot man u're a lifesaver!

9. Zarkon

np

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