Partition Theorem Homework: Solving for the Partition Function and Energy States

[Calpalned]

Homework Statement

Homework Equations

Partition function = $\frac{z_{i+1}}{z_i}$
$z = \Sigma_{j=1}^\infty g_j e^{\frac{-(E_j - E_i)}{KT}}$
$g_j = 2(j^2)$

The Attempt at a Solution

I should get 2, but I keep getting $2 + 8e^7.8 + ...$
I used $K = 1.38 \times 10^-23$ and I converted electron volts to J (1eV = $1.602 \times10^-19$J)

 

[Calpalned]

Homework Statement

View attachment 90647

Homework Equations

Partition function = $\frac{z_{i+1}}{z_i}$
$z = \Sigma_{j=1}^\infty g_j e^{\frac{-(E_j - E_1)}{KT}}$
$g_j = 2(j^2)$

The Attempt at a Solution

I should get 2, but I keep getting $2 + 8e^7.8 + ...$
I used $K = 1.38 \times 10^-23$ and I converted electron volts to J (1eV = $1.602 \times10^-19$J)

Actually what is $E_j$ and $E_1$? Isn't E_1 = 13.6?