Question

HELP ASAP

Answer 1

Firstly, what does it mean if a sequence converges, or diverges?

Answer 2

convergent sequence has a limit — that is, it approaches a real number. A divergent sequence doesn’t have a limit. @davejavous

Answer 3

please help and stay until the end

Answer 4

@DanJS

Answer 5

I will stay don't worry :)

Answer 6

okgreat if we could go a little faster that'd be great I really just need to get to the correct answer ASAP i have a few other questions to ask you too!:-)

Answer 7

So you should be able to see that it is a geometric progression? Can you find the common ratio, r?

Answer 8

can you just show me please i need to go soon not trying to be rude but please just show me the whole process that would be most beneficial because i know how i learn best

Answer 9

or someone please

Answer 10

The sequence is a geometric progression, which means it is in the form:
\[ a, ar, ar^2, ar^3 ... \]
We know that the first term from the question:
\[ a = 108 \]
The ratio, r is found by doing:
\[ r = \frac{a_{n+1}}{a_n} \]\[ \therefore r = \frac{-18}{108} \]\[ r = -\frac{1}{6}\]
Because we multiply by -1/6 each time we know that the following terms will just get smaller and smaller towards 0.

This is because of the following limit:
\[\lim_{n \rightarrow \infty} x^n = 0 \;\; for \;\;-1 \lt x \lt 1\]
Because r is in the range -1<x<1 then it will converge to 0, and 108 x 0 = 0

Hence, the answer is Converges, 0

Answer 11

wow thanks so much! That helped so so much. I will write that down in my noted now. Can you help with another too? your explanations rally help me learn and understand so much that can i have help with another @davejavous

Answer 12

Yes of course I'll help :D

Answer 13

thank you! Ill start a new post and tag yu.

Answer 14

@iwanttogotostanford