Direct Comparison Test - Another Example 2

[Kajehart]

Brilliant! I never would've thought of using 1/n by using n^3+n^3!

[naclandpepper]

at 1:06 why did u change n^3+1 to n^3 +n^3

[Beyndestiny]

The rules are that it can only be proven it diverges IF the original series (An) is something that is larger than the series that you compare it to (Bn). In the FIRST case whereby we find that (1/n) is a divergent p series, we cannot use this as something to prove it diverges BECAUSE 1/n (Bn) is something that is larger to our (An). What he is trying to do is find a RELATION to the series and the comparison by making a smaller comparison to our original. Then only can it be proven by Comparison test.

[leviraby]

Couldn't you have just compared it to the sum of 1/n? Why did compare your original function to 1/(n^3 + n^3)^1/3 ?

[ohyourgodwhat]

I thought An needs to be greater than Bn? But you justified that it is greater?

[lshq]

shouldn't (an) be greater than (bn) for it to diverge? patrickJMT 

[jacobroeland]

Why does 1/n with n=infinity go to infinity? Shouldn't it go to zero?

[adameveritt]

what would be the case if you had n as the numerator

[Erinxxxxxx]

Why is this divergent? Does 1/n not converge to 0?

[itempus]

@antis0cialist It does go to 0. 1/(a really big number) is 0.