sigma notation

Question

Use sigma notation to re-write the sum: 1/4 + 3/8 + 7/16 +...+ 31/64

Answer 1

The denominators are all powers of 2.

 

Each numerator is one less than a power of 2.

 

1/4 + 3/8 + 7/16 + 15/32 + 31/64 = ∑_{(from n=2 to n=6)} [(2^n-1 - 1)/2ⁿ]