计算:1+1/2+1/2²;+1/2³;+.+1/2^100的值
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![计算:1+1/2+1/2²;+1/2³;+.+1/2^100的值](/uploads/image/z/14909370-42-0.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9A1%2B1%2F2%2B1%2F2%26%23178%3B%3B%2B1%2F2%26%23179%3B%3B%2B.%2B1%2F2%5E100%E7%9A%84%E5%80%BC)
计算:1+1/2+1/2²;+1/2³;+.+1/2^100的值
计算:1+1/2+1/2²;+1/2³;+.+1/2^100的值
计算:1+1/2+1/2²;+1/2³;+.+1/2^100的值
设A=1+1/2+1/2²;+1/2³;+.+1/2^100
则2A=2+1+1/2+1/2²+………+1/2^99
∴2A-A=﹙2+1+1/2+1/2²+………+1/2^99﹚-﹙1+1/2+1/2²;+1/2³;+.+1/2^100﹚
∴A=2-1/2^100
=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024+1/2048+1/4096+1/8192+1/16384+1/32768+1/65536+1/131072+1/262144+1/524288+1/1048576+...........1
=1又2^100-1/2^100