1/2加1/4加1/8加1/16加1/32加1/64加1/128加1/256怎么简便
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1/2加1/4加1/8加1/16加1/32加1/64加1/128加1/256
=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=1/2^1+1/2^2+1/2^3+1/2^4+1/2^5+1/2^6+1/2^7+1/2^8
let
S=1/2^1+1/2^2+1/2^3+1/2^4+1/2^5+1/2^6+1/2^7+1/2^8 (1)
(1/2)S=1/2^2+1/2^3+1/2^4+1/2^5+1/2^6+1/2^7+1/2^8+1/2^9 (2)
(1)-(2)
(1/2)S = 1/2^1 - 1/2^9
S = 1 - 1/2^8
= 255/256
=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=1/2^1+1/2^2+1/2^3+1/2^4+1/2^5+1/2^6+1/2^7+1/2^8
let
S=1/2^1+1/2^2+1/2^3+1/2^4+1/2^5+1/2^6+1/2^7+1/2^8 (1)
(1/2)S=1/2^2+1/2^3+1/2^4+1/2^5+1/2^6+1/2^7+1/2^8+1/2^9 (2)
(1)-(2)
(1/2)S = 1/2^1 - 1/2^9
S = 1 - 1/2^8
= 255/256
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