Worked example: sequence convergence/divergence (video) | Khan Academy

Want to join the conversation?Log inSort by:Robert Checco10 years agoPosted 10 years ago. Direct link to Robert Checco's post “I am confused how at 2:00...”I am confused how at 2:00 Sal is sure that is converges. I understand that the N^2 is going to grow at the faster rate, but wont the numerator become larger and larger than the denominator? In the denominator as "n" gets larger and larger the 10n is being subtracted from n^2. Whereas on the top the "n" is recieving addition by 9n. At what point is the "10n" or the "8n" enough to change the limiting value.Button navigates to signup page•Comment on Robert Checco's post “I am confused how at 2:00...”(16 votes)Creeksider10 years agoPosted 10 years ago. Direct link to Creeksider's post “The key is that the absol...”The key is that the absolute size of 10n doesn't matter; what matters is its size relative to n^2. When n=100, n^2 is 10,000 and 10n is 1,000, which is 1/10 as large. When n=1,000, n^2 is 1,000,000 and 10n is 10,000. We increa...