简便计算:1/2+3/4+7/8+15/16+31/32+63/64+127/218
问题描述：
简便计算:1/2+3/4+7/8+15/16+31/32+63/64+127/218
答
1/2+3/4+7/8+15/16+31/32+63/64+127/128=1-1/2+1-1/4+1-1/8+1-1/16+1-1/32+1-1/64+1-1/128=7-(1/2+1/4+1/8+1/16+1/32+1/64+1/128)=7-1/2(1-1/2^7)/(1-1/2)=7-127/128=6又1/128