1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256+511/512如何计算
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1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256+511/512如何计算
设
a=1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256
b=1/2+1/4+1/8+1/16+ 1/32+ 1/64+ 1/128+ 1/256
那么a+b=8
b+1/256=1/2+1/4+1/8+1/16+ 1/32+ 1/64+ 1/128+ (1/256+1/256)
=1/2+1/4+1/8+1/16+ 1/32+ 1/64+( 1/128+ 1/128)
=1/2+1/4+1/8+1/16+ 1/32+ (1/64+ 1/64)
=……
=1
所以b=1-1/256
a=8-b=8-(1-1/256)
=7+1/256
或者
an=(2^n-1)/2^n=1-1/2^n
Sn=8*1-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256)
=8-0.5(1-0.5^8)/1-0.5
=8-255/256
=1793/256
a=1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256
b=1/2+1/4+1/8+1/16+ 1/32+ 1/64+ 1/128+ 1/256
那么a+b=8
b+1/256=1/2+1/4+1/8+1/16+ 1/32+ 1/64+ 1/128+ (1/256+1/256)
=1/2+1/4+1/8+1/16+ 1/32+ 1/64+( 1/128+ 1/128)
=1/2+1/4+1/8+1/16+ 1/32+ (1/64+ 1/64)
=……
=1
所以b=1-1/256
a=8-b=8-(1-1/256)
=7+1/256
或者
an=(2^n-1)/2^n=1-1/2^n
Sn=8*1-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256)
=8-0.5(1-0.5^8)/1-0.5
=8-255/256
=1793/256
1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256+511/512如何计算
如何计算1/2+3/4+7/8+15/16+31/32+63/64+127/128怎么简便计算?
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