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 2 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.
 2 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.

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bahrom7893
 2 years ago
Best ResponseYou've already chosen the best response.1@satellite73 can u help, plz?

bahrom7893
 2 years ago
Best ResponseYou've already chosen the best response.1@Zarkon can u take a look at this too?

Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.3the sum up to N1 is a finite sum so it doesn't contribute to the convergence or divergence of the series.

Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.3is assume \(\sum a_n\) converges then \[\sum_{k=1}^{\infty}b_n=\sum_{k=1}^{N1}b_n+\sum_{k=N}^{\infty}b_n\] \[=\sum_{k=1}^{N1}b_n+\sum_{k=N}^{\infty}a_n\] since \(\sum_{k=1}^{N1}b_n\) is finite and \(\sum a_n\) converge...so does \(\sum b_n\)

bahrom7893
 2 years ago
Best ResponseYou've already chosen the best response.1tnx a lot man u're a lifesaver!
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