Question

1/2+1/4+1/8+1/16+1/32+1/64+1/128等于？为什么

Answer 1

解：
从上可以看出，该数列是一个等比数列
公比是：q = 1/2
首项是1/2，尾项是1/128
an = a1 ×[q^(n-1)]
an = 1/2 ×[1/2^(n-1)]
an =( 1/2)^n
1/128是当n =7时的数
所以，前7项之和为：
sn = [ a1（1-q^n） ] ÷ （1 -q）
= 1 - （1/2）^7
= 1- 1/128
= 127/ 128 （128分之127）

Answer 2

1/2+1/4+1/8+1/16+1/32+1/64+1/128
=1-1+1/2+1/4+1/8+1/16+1/32+1/64+1/128
=1-1/2+1/4+1/8+1/16+1/32+1/64+1/128
=1-1/4+1/8+1/16+1/32+1/64+1/128
=1-1/8+1/16+1/32+1/64+1/128
=1-1/16+1/32+1/64+1/128
=1-1/32+1/64+1/128
=1-1/64+1/128
=1-1/128
=127/128