Question

Determine whether the sequence An=ln(7n^(2)+7)-ln(n^(2)+7) converges or diverges. If it converges, provide the exact value to which the sequence converges

Answer 1

the only method i know of with any degree of confidence is that ratio method

Answer 2

take the limit of an+1/an

Answer 3

keep in mind that we might be able to simplify this with log rules

log(a/b) = loga - logb

Answer 4

ln(7n^(2)+7) - ln(n^(2)+7)

ln (7n^(2)+7)/(n^(2)+7)

ln (7) + ln(n^(2)+1)/(n^(2)+7)

Answer 5

as n gets large, this reduces to ln(7) + ln(n^2/n^2)

Answer 6

i guess i know a different approach than the ratio stuff :)

Answer 7

let me know what youthink of it ...

Answer 8

It would be ln(7)+ln(1), ln(1)=0, leaving me with ln(7)?

We didn't go over any examples like this in class and this specific lecture was a video the prof posted online so we could catch up, so this is new

Answer 9

Yup, it worked, thank you so much!!

Answer 10

youre welcome :)