1/2+1/4+1/8+1/16+········+1/256(简便计算)

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1/2+1/4+1/8+1/16+········+1/256(简便计算)1/2+1/4+1/8+1/16+········+1/256(简便计算)1/2+1/4+1/8+1/16+········+

1/2+1/4+1/8+1/16+········+1/256(简便计算)
1/2+1/4+1/8+1/16+········+1/256(简便计算)

1/2+1/4+1/8+1/16+········+1/256(简便计算)
这是一个等比数列求和,首相(a1)为1/2 公比(q)为1/2
等比数列求和公式:Sn=a1(1-q^n)/(1-q)
其中n为项数比如a1项数就为1
a1=1/2 a2=1/4 a3=1/8········a8=1/256
至于这个256是a8是怎么得出的256开个平方根就行了.
所以Sn=1/2(1-(1/2)^8)/(1-1/2)=255/256

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这是一个等比数列,公比是1/2,首项是1/2,运用公式Sn=a1(1-qn)/1-q=1/2(1-1/2n)/1/2
=1-1/2n其中n=8.所以最后结果为255/256

1/2+1/4+1/8+1/16+1/32+...+1/256
=1/2+1/4+1/8+1/16+1/32+...+1/256+1/256-1/256
=1/2+1/4+1/8+1/16+1/32+...+1/128+1/128-1/256
=1/2+1/4+1/8+1/16+1/32+1/64+1/64-1/256
=1/2+1/4+1/8+1/16+1/32+1/32-1/256
=……
=1-1/256=255/256

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