Question

Determine whether the sequence converges or diverges. If it converges, give the limit.

48, 8,4/3 ,2/9 , ...

Answer 1

it looks geometric, i.e. you multiply each term by the same number to get the next term

Answer 2

looks like you are dividing by 6 each time, i.e. it is
\[48,48\times \frac{1}{6},48\times (\frac{1}{6})^2,....\]

Answer 3

well how do you knw if they diverge or converge? This wasnt in my lesson

Answer 4

since \(r=\frac{1}{6}<1\) it converges to 0 i.e. the terms get closer and closer to 0

Answer 5

in fact the sum converges as well, i.e. the series converges

Answer 6

oh okay!! thank you!