1/6+1/12+1/24+``````+1/990简便计算
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![1/6+1/12+1/24+``````+1/990简便计算](/uploads/image/z/430549-61-9.jpg?t=1%2F6%2B1%2F12%2B1%2F24%2B%60%60%60%60%60%60%2B1%2F990%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97)
1/6+1/12+1/24+``````+1/990简便计算
1/6+1/12+1/24+``````+1/990简便计算
1/6+1/12+1/24+``````+1/990简便计算
an = (1/6)(1/2)^(n-1)
Sn = a1+a2+...+an
= (1/3)( 1- (1/2)^n )
1/6+1/12+1/24+...+1/990
=S165
=(1/3)( 1- (1/2)^165 )