Need help with limits | Mathematics | Page 1

vocal blaze Feb 28, 2026, 1:07 PM

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prove the limit of a sequence by definition using the ε−N approach.

rare kilnBOT Feb 28, 2026, 1:07 PM

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vocal blaze Feb 28, 2026, 1:08 PM

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ok, so i get the limit which is -1

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then i put into a module where | An + 1 | = ...

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then i put everything over the same denominator

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and that's it

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idk what to do next

sharp moss Feb 28, 2026, 3:06 PM

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you know what this really sucks to prove

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but there's something you can do here

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find the minimum (or infimum) of the roots in the denominator

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then bound the entire modulus to that

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but keep the numerator

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this should easen it

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then you can multiply by the conjugate after pulling out the factor below if that helps

sharp moss Feb 28, 2026, 3:07 PM

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sharp moss find the minimum (or infimum) of the roots in the denominator

if they exist

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but because sequences are from N to R surely at least the infimum does exist

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i don't see the denominator turning into a straight 0 from the addition of the minimums so that's good

vocal blaze Feb 28, 2026, 3:50 PM

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jesus chirst

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well

lament trench Mar 1, 2026, 12:22 AM

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Simply the denominator and numerator to the highest powers

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For the numerator (n^2)^(1/3)=n^(2/3) which has a lower power than the -n^1 so u can simply the top to -n

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For the denominator (n^2)^.5=n^1 which has a higher power than (n^4)^.2 so the bottom is n

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Meaning at infinity the limit is -n/n=-1

#Need help with limits