# How do you write the expression for the nth term of the sequence given 1+1/2, 1+3/4, 1+7/8, 1+15/16, 1+31/32,...?

${n}^{t h}$ term of the sequence under consideration is $1 + \frac{{2}^{n} - 1}{2} ^ n$
Observe that each term has two components , one just $1$ and the other, whose denominators are in the sequence $2 , 4 , 8 , 16 , \ldots .$ and numerator is just one less than the denominator .
As the ${n}^{t h}$ term of the sequence $2 , 4 , 8 , 16 , \ldots .$ is ${2}^{n}$
${n}^{t h}$ term of the sequence under consideration is $1 + \frac{{2}^{n} - 1}{2} ^ n$