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The sum sum ( k = 1 ) ^ ( 20 ) k ...

The sum ` sum _ ( k = 1 ) ^ ( 20 ) k ( 1 ) / ( 2 ^ k ) ` is equal to ` l - (11) /(m ^ ( 19 )) `. The value of ` ( l + m ) ` is ______ .

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` S = (1 ) /(2) + (2 )/(2^ 2 ) + …. + (20)/(2^(20)) `
` (S)/(2) = (1)/(2^2 ) + ( 2 ) /( 2 ^ 3 ) + ….. + (20)/( 2 ^( 21 )) `
` (S)/(2) = (1)/(2) + ( 1 ) /(2 ^ 2 ) + (1 ) /(2^ 3 ) + …… + (1 ) /(2^( 20)) - (20)/(2 ^ (21) ) `
` = (1 )/(2) ( 1 - ((1)/(2))^ (20))/( 1 - (1 ) /(2) ) - (20)/(2^(21))" " S= 2 - (22)/(2^(20)) = 2 - (11)/(2^(19)) `
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