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13:00 Example c) should multiply numerator and denominator by n^(-1/3) not "n root 1/3 " because "n root 1/3 " is equivalent to n^3. However n^(1/3) * n^(-1/3) = n^(0) which is now equal to 1. However, the limit still converges on 1.
I don't understand why n would become smaller (i.e. n*(n-1)*n(n-2), wouldn't it be 1!, 2!, 3!, 4! ... ? 16:00 n! simply increases based on a_n?
What will happen if (-1)^n as n approaches infinity?
thank you
13:00can we use l'hopital rule?
I don't see why not! You would still get the limit of 1, which would still indicate convergence. Great idea!
13:00 Example c) should multiply numerator and denominator by n^(-1/3) not "n root 1/3 " because "n root 1/3 " is equivalent to n^3. However n^(1/3) * n^(-1/3) = n^(0) which is now equal to 1. However, the limit still converges on 1.
I don't understand why n would become smaller (i.e. n*(n-1)*n(n-2), wouldn't it be 1!, 2!, 3!, 4! ... ? 16:00 n! simply increases based on a_n?
What will happen if (-1)^n as n approaches infinity?
thank you
13:00
can we use l'hopital rule?
I don't see why not! You would still get the limit of 1, which would still indicate convergence. Great idea!