1/2+1/4+1/8+...+1/2n=?
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S = 1/2+1/4+1/8+...+(1/2)^n (1)
(1/2)S = 1/4+1/8+1/16+...+(1/2)^(n+1) (2)
(1)-(2)
(1/2)S = 1/2 - (1/2)^(n-1)
S = 1 - (1/2)^n
1/2+1/4+1/8+...+(1/2)^n =S = 1 - (1/2)^n
(1/2)S = 1/4+1/8+1/16+...+(1/2)^(n+1) (2)
(1)-(2)
(1/2)S = 1/2 - (1/2)^(n-1)
S = 1 - (1/2)^n
1/2+1/4+1/8+...+(1/2)^n =S = 1 - (1/2)^n
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