1/2+1/4+1/8+1/16+1/32+1/64+1/128 简便运算

1/2+1/4+1/8+1/16+1/32+1/64+1/128 简便运算
1/2+1/4+1/8+1/16+1/32+1/64+1/128 简便运算

1/2+1/4+1/8+1/16+1/32+1/64+1/128 简便运算
...等比数列 从面积上面来看,一个正方形被不断等分
1-1/128 =127/128

1/2+1/4+1/8+1/16+1/32+1/64+1/128
=(1/2)^1+(1/2)^2+(1/2)^3+(1/2)^4+(1/2)^5+(1/2)^6+(1/2)^7
=(1/2)^1×[1-(1/2)^7]/(1-1/2)
=1-(1/2)^7
=1-1/128
=127/128