hey got problem with series (1 Viewer)

[red802]

Hey, i got a problem with this question

write each recuurring decimal as a fraction

a) 2.888888888......
b)0.232323232323....

Use the limiting sum formula

show working out

 

[SoulSearcher]

a) 2.8888888.............. = 2 + 0.88888............ = 2 + (0.8 + 0.08 + 0.008 + ... )
therefore, 2.888........... = 2 + 0.8/(1-0.1), letting a = 0.8, r = 0.1
= 2 + 0.8/0.9 = 26/9

b) 0.23232323.... = 0.23 + 0.0023 + 0.000023 ...
= 0.23/(1-0.01), letting a = 0.23, r = 0.01
= 0.23/0.99
= 23/99

 

[red802]

also i got some other problems, what about 1.0151515151515

and also

find the difference between the limiting sum and the sum of 6 terms of the series
a) 56-28+14-....

 

[SoulSearcher]

1.01515.... = 1 + 0.015 + 0.00015 + 0.0000015 ...
= 1 + 0.015/(1-0.01)
= 1 + 0.015/0.99
= 1 + 15/990
= 1 + 1/66
= 67/66

the series 56-28+14-7 .... has first term 56 and ratio -0.5
therefore limiting sum is 56/(1+0.5) = 56/1.5 = 112/3
now the sum of the first 6 terms of the series is equal to
56 - 28 + 14 - 7 + 3.5 - 1.75 = 36.75 = 147/4
therefore difference is 112/3 - 147/4 = 7/12