bahrom7893
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
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@satellite73 can u help, plz?
bahrom7893
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@imranmeah91 ?
imranmeah91
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what class is it?
bahrom7893
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Cal 2
bahrom7893
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@Zarkon can u take a look at this too?
Zarkon
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the sum up to N-1 is a finite sum so it doesn't contribute to the convergence or divergence of the series.
Zarkon
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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 \(\sum b_n\)
bahrom7893
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tnx a lot man u're a lifesaver!
Zarkon
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np