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bahrom7893

  • 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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  1. bahrom7893
    • 2 years ago
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    @satellite73 can u help, plz?

  2. bahrom7893
    • 2 years ago
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    @imranmeah91 ?

  3. imranmeah91
    • 2 years ago
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    what class is it?

  4. bahrom7893
    • 2 years ago
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    Cal 2

  5. bahrom7893
    • 2 years ago
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    @Zarkon can u take a look at this too?

  6. Zarkon
    • 2 years ago
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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.

  7. Zarkon
    • 2 years ago
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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 \(\sum b_n\)

  8. bahrom7893
    • 2 years ago
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    tnx a lot man u're a lifesaver!

  9. Zarkon
    • 2 years ago
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    np

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