0.19191919.(19循环)
=0.19+0.0019+0.000019+…
可看作首项为0.19,公比为0.01的等比数列的前n项和,n→∞
所以
0.19191919.(19循环)
=0.19+0.0019+0.000019+…
=0.19(1-0.01^n)/(1-0.01),n→∞
=19/99
0.19191919.(19循环)
=0.19+0.0019+0.000019+…
可看作首项为0.19,公比为0.01的等比数列的前n项和,n→∞
所以
0.19191919.(19循环)
=0.19+0.0019+0.000019+…
=0.19(1-0.01^n)/(1-0.01),n→∞
=19/99