​ How many students are identified to have measles in all at the end of the 6th day of the outbreak?

1st day:8

2nd day: 16

3rd day: 32

4th day:64

5th day:128

6th day: 256

Now, we have 8+16+32+64+128+256.

If we divide each number by 8, we get:

1+2+4+8+16+32=63

But, we have to multiply back again by 8, because we divided by 8.

Thus, the answer is \(63*8=\boxed{504}\)

Thanks, tertre.....

Here's the "short way"  to find the sum, S₆, at the end of the 6th day....we have that

Sum at any time  =  Initial value  [ 1  - r^n ] / [ 1  - r ]

The initial value is 8

The common ratio, r  = 2

n = the number of days

So we have

S₆  =  8  [ 1 - 2^6]  / [ 1 - 2 ]   =   504  students