简便计算:1/2+3/4+7/8+15/16+31/32+63/64+127/218

简便计算:1/2+3/4+7/8+15/16+31/32+63/64+127/218
简便计算:1/2+3/4+7/8+15/16+31/32+63/64+127/218

简便计算:1/2+3/4+7/8+15/16+31/32+63/64+127/218
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

原式=1-1/2 + 1-1/4 + 1-1/8+....+1-1/128
=1 + 1 +...+1 - (1/2 + 1/4 + ..+1/128)
= 7 - (1/2-1/256)/(1-1/2)
= 7 - 127/128

1/2+3/4+7/8+15/16+31/32+63/64+127/218
=(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)
=7-127/128
=769/128