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

1 Answer
Apr 17, 2018

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.