Question

Please Help!!

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

48, 8, 4/3, 2/9

Answer 1

@SolomonZelman @precal @paki

Answer 2

hmm what does it mean to converge?

Answer 3

It means that the sum of the individual terms of the sequence from n=0 to infinity equates to some finite number.

Answer 4

@jdoe0001

Answer 5

yes... so .... notice the numbers.... from 48 to 8 is a division by 6
from 8 to 4/3 is a division by 6
from 4/3 to 2/9 is a division by 6

so we could say that \(\bf a_1 = 48\quad r=6\)
thus \(\Large \bf S=\Sigma_{i=0}^\infty\ a_1{\color{brown}{ r}}^i\implies \cfrac{a_1}{1-{\color{brown}{ r}}}\implies \cfrac{48}{1-{\color{brown}{ 6}}}\)

Answer 6

and that reaches a limit, a finite value, thus it "converges"

Answer 7

hmm actually.... wait.. a sec... I may have spoken too soon

our "r" should be 1/6 not 6 lemme redo that

Answer 8

1/6 since is a "division" by 6

Answer 9

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

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

Converges; 288/5

Converges; 0

Diverges

Converges; -12432

Answer 10

those are my only choices..

Answer 11

oh ok

Answer 12

\(\large \bf S=\Sigma_{i=0}^\infty\ a_1{\color{brown}{ r}}^i\implies \cfrac{a_1}{1-{\color{brown}{ \frac{1}{6}}}}\implies \cfrac{48}{1-{\color{brown}{ \frac{1}{6}}}}\implies \cfrac{48}{\frac{5}{6}}\implies \cfrac{48}{1}\cdot \cfrac{6}{5}\)

Answer 13

hmm got a bit truncated so \(\bf \large {
S=\Sigma_{i=0}^\infty\ a_1{\color{brown}{ r}}^i\implies \cfrac{a_1}{1-{\color{brown}{ \frac{1}{6}}}}\implies \cfrac{48}{1-{\color{brown}{ \frac{1}{6}}}}\implies \cfrac{48}{\frac{5}{6}}
\\ \quad \\
\implies \cfrac{48}{1}\cdot \cfrac{6}{5}
}\)

Answer 14

what would that give you?

Answer 15

so its 288/5 as the limit

Answer 16

yeap... it has a finite end. and thus it converges, it converges at 288/5

Answer 17

thank you :)