`1 + 1/2, 1 + 3/4, 1 + 7/8, 1 + 15/16, 1 + 31/32` Write an expression for the apparent nth term of the sequence. (assume that n begins with 1)

When we look at the sequence as a whole, we see that there is always a 1 added to a fraction, and this is important. So we try to see if there is any connection between the fractions. 1/2, 3/4, 7/8, etc. We see that the difference between the numerator and the denominator is always 1. But what is the relationship between each denominator? If you take the denominators: 2, 4, 8, 16, etc, you see that they are all powers of 2. In addition, the numerator would be that power of 2 minus 1. 2 is 2^1, 4 is 2^2, 8 is 2^3, etc. Therefore, the sequence for the nth term would be 1+[(2^n-1)/2^n].