How can I prove the following? 1)$$\sum_{k=0}^{\infty}\frac{1}{F_{2k+1}}=\frac{\sqrt{5}}{4}\theta_{2}^{2}(0,\frac{3-\sqrt{5}}{2}),$$ 2)$$\sum_{k=0}^{\infty}\frac{1}{F_{k}^{2}}=\frac{5}{24}(\theta_{2}^{4}(0,\frac{3-\sqrt{5}}{2})-\theta_{4}^{4}(0,\frac{3-\sqrt{5}}{2})+1),$$
Are there good resources in this case?