1+ 1/2 + 3/4 + 7/8 + 15/16简便计算,

问题描述:

1+ 1/2 + 3/4 + 7/8 + 15/16
简便计算,

1+1-1/2+1-1/2^2+...+1-1/2^4=5-(1/2+1/2^2+1/2^3+1/2^4)=5-15/16=65/16

=1+1-1/2+1-1/4+1-1/8+1-1/16
=5-1/2-1/4-1/8-1/16
=5-(1/2+1/16)*4/2
=5-9/8
=31/8

(16+8+12+14+15)/16=65/16