Question

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,...`?

Answer 1

`n^(th)` term of the sequence under consideration is `1+(2^n-1)/2^n`

Explanation:

Observe that each term has two components , one just `1` and the other, whose denominators are in the sequence `2,4,8,16,....` and numerator is just one less than the denominator .

As the `n^(th)` term of the sequence `2,4,8,16,....` is `2^n`

`n^(th)` term of the sequence under consideration is `1+(2^n-1)/2^n`