Question

X Y
1 1
2 1+2
3 1+2+4
4 1+2+4+8

Answer 1

Write an equation that relates X and Y

Answer 2

\[y=\sum _{n=1}^x 2^{n-1} \]\[\text{Table}\left[\left\{y=\sum _{n=1}^x 2^{n-1}\right\},\{x,1,5\}\right] \]{ 1, 3, 7, 15, 31 }

Answer 3

The last two lines above were from Mathematica v9 Home Edition.