there are two methods of doing this each method can take upto 50 Secs

First Method

1/3= 33.33%

1/9= 11.11%

1/27 will be 1/9( 33.33%) 3.70 %

addding we get it will be nearly equal to 49 % so the answer will be what

Each choice can be read as

A 0 and 1/9 can be read as 0% to 11% ( No)

B.1/9 and 1/3 can be read as 11% to 33% ( No)

C.1/3 and 8/9 can be read as 33% to 88% ( Ok seems in our range)

D.8/9 and 4/3 can be read as 88% to 133% ( No)

E. 4/3 and 2 can be read as 133% to 200% ( No)

Second method

if we can see the series is as GP then sum is given by

a{1-(r)^n}/{1-r}

a= 1/3 , r=1/3

Now 1/3{1-1/27}/{1-1/3}

={26/27*3}2/3

= 13/27

ok so 13/26 = 1/2=.5 and 13/26>13/27 so thus value is slightly less than .5

So only option C it says between .333 to .8888

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Abhimanyu