1/3+1/9+1/27+1/81+……+1/177147

问题描述:

1/3+1/9+1/27+1/81+……+1/177147

设s=1/3+1/9+1/27+1/81+……+1/177147
3s=1+1/3+1/9+1/27+1/81+……+1/59049
3s-s=2s=1-1/177147
s=(1-1/177147)/2=88573/177147
所以1/3+1/9+1/27+1/81+……+1/177147 =88572/177147

令M=1/3+1/9+1/27+1/81+……+1/177147…①
则1/3M=1/9+1/27+1/81+……+1/177147+1/531441…②
由①-②得M-1/3M=1/3-1/531441
即2/3M=177146/531441
∴M=88573/177147