How do I solve -LSB- math -RSB- \ lim _ -LCB- x \ rightarrow 0 -RCB- \ left | \ frac -LCB- x +1 -RCB- -LCB- x-1 -RCB- \ right | -LSB- / math -RSB-
How do I solve -LSB- math -RSB- \ lim \ limits _ -LCB- n \ to \ infty -RCB- \ left -LRB- \ frac -LCB- x -RCB- -LCB- 1-x ^ 2 -RCB- + \ frac -LCB- x ^ 2 -RCB- -LCB- 1-x ^ 4 -RCB- + ... + \ frac -LCB- x ^ -LCB- 2 ^ n -RCB- -RCB- -LCB- 1-x ^ -LCB- 2 ^ -LCB- n +1 -RCB- -RCB- -RCB- \ right -RRB- -LSB- / math -RSB- where -LSB- math -RSB- 0 < x < 1 -LSB- / math -RSB- ?