Math Help - Guess a simple for for P_n for this sequence

1. Guess a simple for for P_n for this sequence

I just need to find the pattern to a), which i am having the hardest time doing.

P2 = 2/3
P3 = 5/8
P4 = 3/5
P5 = 7/12
P6 = 4/7
P7 = 9/16

2. Re: Guess a simple for for P_n for this sequence

Hello, hcuk!

$\text{Find the }n^{th}\text{ term: }\:\frac{2}{3},\:\frac{5}{8},\:\frac{3}{5},\:\frac {7}{12},\:\frac{4}{7},\:\frac{9}{16}$

$\text{We have: }\:\begin{array}{c|cccccc}n & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \\[-4mm] P_n & \frac{4}{6} & \frac{5}{8} & \frac{6}{10} & \frac{7}{12} & \frac{8}{14}& \frac{9}{16}\end{array}$

$\text{Therefore: }\:P_n \:=\:\frac{n+3}{2(n+2)}$

3. Re: Guess a simple for for P_n for this sequence

Originally Posted by Soroban
Hello, hcuk!

$\text{We have: }\:\begin{array}{c|cccccc}n & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \\[-4mm] P_n & \frac{4}{6} & \frac{5}{8} & \frac{6}{10} & \frac{7}{12} & \frac{8}{14}& \frac{9}{16}\end{array}$

$\text{Therefore: }\:P_n \:=\:\frac{n+3}{2(n+2)}$
Hello Soroban,