need help-series/sequence (1 Viewer)

[dawma88]

i cant do this question:

find 0.2777777....etc as a rational number using the infinte series ?


i can do similar quesstions but this one has got me stuck

so thanx in advance

 

[insert-username]

0.27777 = 0.2 + 0.07 + 0.007 + 0.0007 + .....

The [0.07 + 0.007 + 0.0007] is a geometric series with first term 0.07 and common ratio 1/10. The sum to infinity of a geometric series with common ratio less than 1 and greater than 0 is given by:

S = a/(1-r)

So the decimal is equal to:

= 0.2 + 0.07/(1 - 1/10)

= 0.2 + 0.07/(9/10)

= 0.2 + 0.7/9

= 1/5 + 7/90

= 25/90

= 5/18

I checked the answer by doing the division, and it's right. Hope that helps.


I_F

 

[dawma88]

hey thanx alot buddy !

appreciate u helping me

 

[insert-username]

No problemo. Always happy to help out.


I_F