How can I solve this? $$\sum_{k=1}^n \frac{2^{2^{k-1}}}{1-2^{2^k}}$$
Actually I tried many direction, but failed. Please give me some right direction.
$$\sum_{k=1}^n \frac{2^{2^{k-1}}}{1-2^{2^k}} = \sum_{k=1}^n \frac{2^{2^{k-1}}}{(1-2^{2^{k-1}})(1+2^{2^{k-1}})}=\cdots$$