DON'T factor out! (Limit Example 3: Complex Fraction)

[@Kdd160]

Excellent video u explained each and every detail

[@MichaelRothwell1]

Very impressive, with great attention to detail (as usual)! I'm probably being over finicky here, but I think a couple of lines could have been added around 15:35. You showed earlier that if n³-2>n³/2 then n>∛4, but now you need the opposite implication. I noticed this detail because of your avoiding two-way implication signs.

[@CliffStamp]

I often wonder who came up with those approaches, they are often simple when you see it (top is smaller, bottom is bigger, hence the same inequality will hold) but it isn't trivial maybe to come up with that approach.

[@tomatrix7525]

Love these

[@sinan4988]

Is it false? (3n+4)/(n^3-2)

[@tgx3529]

0

[@drpeyam]

Except it is not true for all N that N^3 -2 > N^2. For instance it is false for N = 1. And factoring our would mean to factor out n^2 from the numerator and the denominator, which people usually do in calculus

[@tgx3529]

@@drpeyam Thank you.Yes, N> max (7/epsilon;1).

[@sidharathsharma6197]

Sir please help me with this question. " If ∑uₙ be a divergent series of positive real numbers and sₙ = u₁ + u₂ + u₃ + - - - - + uₙ then show that the series ∑(uₙ / sₙ) is divergent.

[@Superhumanconsciousness]

Use contaposition with cauchy theoreme

[@sidharathsharma6197]

@@aapeli9662 I saw this question in the book I am currently reading. Please help me prove that it is a falsehood , in case it is one.

[@sidharathsharma6197]

@@Superhumanconsciousness Thankyou so much bro!

[@orlandomoreno6168]

It could diverge or not, it doesn't necessarily follow

[@Superhumanconsciousness]

If Un=1 then sum(Un) diverges => sum(Un/(U1+U2+...+Un)=sum(1/n)=hermonic series

[@nullplan01]

Dumb question, but... N has to be a natural number, right? Because in that case, N > cbrt(2) and N > cbrt(4) are equivalent to N >= 2. So N = max {2, ceil(sqrt(4/e))}.

[@drpeyam]

Nah, N doesn’t have to be an integer, it’s n that has to be one

[@Mateusz-Maciejewski]

@@drpeyam But in many textbooks the definition of limit involves N that has to be a positive integer. This is of course equivalent to the definition with any N and is justified, since we deal with natural numbers (indices). If so, we need to use one more condition: N>=1 and use either ceil(sth) or floor(sth)+1.