Question

Find the sum of the infinite geometric series 8+4+2+1...

Answer 1

could you find the common ratio 'r' ?

Answer 2

-2?

Answer 3

the sum for infinite geometric series is
\(\Large S_n = \dfrac{a_1}{1-r} \)

Answer 4

how ?? you know what common ratio is, right ?

Answer 5

the difference between the values?

Answer 6

nopes,
common ratio is the ratio between consecutive terms

r = 2nd term/ 1st term = 3rd term / 2nd term = .... and so on

Answer 7

like if i had 27,9,3,1,....

then r = 9/27 = 3/9 = 1/3

Answer 8

so 0.33?

Answer 9

that was just an example :P


your sequence is
8+4+2+1...

r = ... ?

Answer 10

r = 4/8 = 2/4 = .... ?

Answer 11

0.5? or 2?

Answer 12

its r = 1/2 (which also = 0.5)

now plug in values in the formula

Answer 13

\(a_1\) = 1s term = 8 here

Answer 14

what is a1?

Answer 15

first term is also 8

Answer 16

a1 is the notation for 1st term
and in this sequence it = 8

Answer 17

\(\Large S_n = \dfrac{a_1}{1-r} = \dfrac{8}{1-1/2} = ... ?\)

Answer 18

=4?

Answer 19

sure ?

Answer 20

\(\dfrac{8}{1/2} = 8\times 2\)

Answer 21

16!!! Sorry you are totally right!
THANKYOUUU!!

Answer 22

\(\huge \color{red}{16 ~~\checkmark \quad \ddot \smile}\)