The Student Room Group

Infinite geometric Sequences

After the chart, there is the explanation about the limits and i cant understand it.

if someone could help me and explain the expplanation about the limit (maybe in simple words) I would be really thankful

Thank you :smile:
(edited 9 years ago)
Reply 1
Original post by sabi06
After the chart, there is the explanation about the limits and i cant understand it.


????

are you uploading something?
Reply 2
Original post by sabi06
After the chart, there is the explanation about the limits and i cant understand it.

if someone could help me and explain the expplanation about the limit (maybe in simple words) I would be really thankful

Thank you :smile:


look in the formula above the chart

it says that if you add a lot of terms, in other words n is very very large (1/2)n is practically zero

[raise 1/2 to larger and larger powers]

so the final answer (after tidy is 2)
Reply 3
Original post by TeeEm
????

are you uploading something?

I put a picture...it cant be seen?
Reply 4
Original post by sabi06
I put a picture...it cant be seen?


I do now.

look at my previous post/reply
see if it helps
Reply 5
Original post by TeeEm
look in the formula above the chart

it says that if you add a lot of terms, in other words n is very very large (1/2)n is practically zero

[raise 1/2 to larger and larger powers]

so the final answer (after tidy is 2)

so as n gets larger it gets closer to 2 and therfore the limit is 2 but i didnt understand what zero has to do with it
Reply 6
Original post by sabi06
so as n gets larger it gets closer to 2 and therfore the limit is 2 but i didnt understand what zero has to do with it


As n gets larges, (1/2)^n gets very close to 0. This is where the zero comes into it.
Reply 7
Original post by sabi06
so as n gets larger it gets closer to 2 and therfore the limit is 2 but i didnt understand what zero has to do with it


NO!

(1/2)n becomes practically zero

type in a calculator larger and larger values for n

so if n gets huge

2[1 - (1/2)n ]becomes 2 x 1 =2
Reply 8
Original post by TeeEm
NO!

(1/2)n becomes practically zero

type in a calculator larger and larger values for n

so if n gets huge

2[1 - (1/2)n ]becomes 2 x 1 =2


I understood now. so as n gets bigger it gets closer to 0 and when you plug that into the equation it gets closer to 2....am i right?
why does this happen?
Reply 9
Original post by sabi06
I understood now. so as n gets bigger it gets closer to 0 and when you plug that into the equation it gets closer to 2....am i right?
why does this happen?


(1/2)n becomes practically zero as you put lager and larger n

so The whole thing eventually (in this case) becomes 2 x 1 =2

why does it happen?

well think

0.5 x 0.5 = 0.25 smaller
0.5 x 0.5 x 0.5 = 0.125 even smaller
0.5 x 0.5 x 0.5 x 0.5 = 0.0625 even smaller

0.5 x 0.5 x 0.5 x .... 0.5 x 0.5 x 0.5 = tiny ...
Reply 10
Original post by TeeEm
(1/2)n becomes practically zero as you put lager and larger n

so The whole thing eventually (in this case) becomes 2 x 1 =2

why does it happen?

well think

0.5 x 0.5 = 0.25 smaller
0.5 x 0.5 x 0.5 = 0.125 even smaller
0.5 x 0.5 x 0.5 x 0.5 = 0.0625 even smaller

0.5 x 0.5 x 0.5 x .... 0.5 x 0.5 x 0.5 = tiny ...


thank you, i understood
Reply 11
Original post by sabi06
thank you, i understood


pleasure

Quick Reply

Latest