Expressing a Sum in Sigma Notation: 1 + (2/3) + (3/5) + (4/7) + (5/9)

[VanceFox]

Homework Statement

"Express the following sum in sigma notation:

1 + (2/3) + (3/5) + (4/7) + (5/9)"

Homework Equations

The Attempt at a Solution

I've figured out what they all have in common (1+2=3, 2+3=5, 3+4=7, 4+5=9) but I've been searching through the book and on the internet how to express this.

 

[Broccoli21]

Suppose the kth term is n(k)/d(k). Can you find a pattern to how the numerator and denominator change with k?

 

[VanceFox]

I just figured it out. Apparently I just needed to finally ask for help.

The equation is (i/2i-1) with start i=1 and end at 5.