Why does the infinite sum -LSB- math -RSB- \ displaystyle \ sum _ -LCB- n = 2 -RCB- ^ -LCB- \ infty -RCB- -LRB- -1 -RRB- ^ n \ dfrac -LCB- 1 -RCB- -LCB- \ ln -LRB- n ! -RRB- -RCB- -LSB- / math -RSB- converge ?
Why does the series -LSB- math -RSB- \ displaystyle \ sum _ -LCB- n = 1 -RCB- ^ -LCB- \ infty -RCB- \ dfrac -LCB- \ sqrt -LCB- n +1 -RCB- - \ sqrt -LCB- n -RCB- -RCB- -LCB- n -RCB- -LSB- / math -RSB- converge ?