简算 1+2分之1+4分之1+8分之1+...+64分之1+128分之1
问题描述：
简算 1+2分之1+4分之1+8分之1+...+64分之1+128分之1
答
1/2+1/4+1/8+1/16+1/32+1/64+1/128
=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128-1/128
=1/2+1/4+1/8+1/16+1/32+1/64+1/64-1/128
=1/2+1/4+1/8+1/16+1/32+1/32-1/128
=1/2+1/4+1/8+1/16+1/16-1/128
=1/2+1/4+1/8+1/8-1/128
=1/2+1/4+1/4-1/128
=1/2+1/2-1/128
=1-1/128
=127/128
答
1+1/2+1/4+1/8+...+1/64+1/128
=1+1-1/2+1/2-1/4+1/4-1/8+...+1/32-1/64+/64-1/128
=1+1-1/128
=2-1/128
=255/128
答
令a=1+2分之1+4分之1+8分之1+...+64分之1+128分之1则两边乘22a=2+1+2分之1+4分之1+8分之1+...+64分之1相减左边是2a-a=a右边中间相同的减去了a=2-128分之1=1又128分之127所以1+2分之1+4分之1+8分之1+...+64分之1+128...