Question

1/2+1/(2的2次方）+1/（2的3次方）+1/（2的4次方）+…+1/2的n次方的值为_______

试求5/6+11/12+23/24+47/48+95/96+191/192+383/384+767/768+1535/1536的值

Answer 1

解答：
（1）1/2+1/(2的2次方）+1/（2的3次方）+1/（2的4次方）+…+1/2的n次方的值为_______
1-1/2的n次方
（2）5/6+11/12+23/24+47/48+95/96+191/192+383/384+767/768+1535/1536
=1-1/6+1-1/12+1-1/24+1-1/48+1-1/96+1-1/192+1-1/384+1-1/768+1-1/1536
= 9-(1/6+1/12+1/24+1/48+1/96+1/192+1/384+1/768+1/1536)
=9-(1/3-1/1536)
=9-1/3+1/1536
化简可以自己解决了吧。