Question

Find the sum of the infinite geometric series in which a1=8 and r= -1/2

Answer 1

use the formula


sum = a
-----------
1-r

Answer 2

is it k? or should i give u the ans

Answer 3

Give me the answer.

Answer 4

sry not 16..........it should be 16/3

Answer 5

put limit n tends infi and u'l see myne formula has nothin wrong......no offence

Answer 6

1/2 to the power n where n is infi will only make it smaller

Answer 7

jose ur goin in wrong direction

Answer 8

cmon answer me (1/2)^infinity is smaller or larger

Answer 9

then 1/2

Answer 10

thats not abt getting it determined but u can say that 1/2^inf must be very small..........so it can be done if u neglect that value

Answer 11

but its very important to note my formula works only when r<1........

Answer 12

the same way inf-1 is inf itself ..........:) don't get frustrated on me....... try to understand

Answer 13

=8 / (3/2) = 8 x2/3 = 16/3


thats it, end of story

Answer 14

thanks elecengineer

Answer 15

the sum of a GP is \[\frac{a(1-r^n)}{1-r}\]

Answer 16

if the absolute value of r is less then 1 , then (1-r^n) ---> 1 , as n-> infinity

Answer 17

so you are multiplying by a factor of 1, and thus why it disappears

Answer 18

r^n gets very small if |r|<1

think of 0.01^1000 , thats 0.01 x 0.01 x 0.01 ... etc 1000 times, it quickly approaches zero

therefore 1-r^n appraoches 1

Answer 19

elecengineer u r very good at explaining :)

Answer 20

likewise if you had (-0.01)^999 ( an odd power so its not even )

then you would get -0.01 x -0.01x ... etc

Answer 21

that would give a very small negative answer, so 1-r^n would be just a tiny bit bigger than 1 , but it would still approach 1

Answer 22

All the above is also explained here:

http://en.wikipedia.org/wiki/Geometric_series

Scroll to "formula" section.

Answer 23

or be very close to 1, so in the limit it is neglected

Answer 24

I stated a wrong equation which lead me to a wrong answer. Sorry for the inconvenience. LOL. I really should start proofreading my works. BTW, thanks for the corrections. Sorry Ishaan. :))