Question

How do you write 3/2 + 5/4 + 9/8 + 17/16 + 33/32 in summation notation?

Answer 1

`sum_1^n(2^k+1)/2^k`

Explanation:

The denominators are progressing geometrically while the numerators are always 1 greater than their denominators. For the `k^(th)` term in the series the denominator is `2^k`. This makes its numerator `2^k+1`. The sum becomes

`sum_1^n(2^k+1)/2^k`

where `n` is the number of terms in the series.