用裂项法解,1/2 = 1 - 1/2,1/4 = 1/2 - 1/4,1/8 = 1/4 - 1/8
原式=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024
=1-1/2+1/2-1/4+1/4-1/8+……+1/512+1/152-1/1024
=1-1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024
=1-1/1024
=1023/1024
等比数列学了没
用裂项法解,1/2 = 1 - 1/2,1/4 = 1/2 - 1/4,1/8 = 1/4 - 1/8
原式=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024
=1-1/2+1/2-1/4+1/4-1/8+……+1/512+1/152-1/1024
=1-1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024
=1-1/1024
=1023/1024
等比数列学了没