Combinatoria con repetición Series paralelas y Números naturales
𝒊 𝒏+𝒎−𝟏 𝑪𝒓𝒏,𝒎 =∑𝒏+𝒎−𝟐 )=( ) 𝒊=𝒎−𝟏 ( 𝒎−𝟏 𝒎
𝒏𝒎+𝟏 𝒏𝒎 𝒏𝒎−𝟏 𝒎 𝒏𝒎−𝟑 𝒎 𝒏𝒎−𝟓 𝒎 𝒏𝒎−𝟕 𝒎 = ⌡+ ⌡+ ( )⌡− ( )⌡+ ( )⌡− ( )⌡±... 𝒎+𝟏 𝟐 𝟏𝟐 𝟏𝟐𝟎 𝟐𝟓𝟐 𝟓 𝟐𝟒𝟎 𝟕 𝟏 𝟑 𝒎=𝟎 𝒎>0 𝒎>1 𝒎>3 𝒎>5 𝒎>7
𝒎 𝒊 𝒎−𝟏 𝒎+𝟏 𝒎+𝒏−𝟐 𝑺𝒎 = {( )} = {( ),( ),( ),…,( )} 𝒎−𝟏 𝒎−𝟏 𝒎−𝟏 𝒎−𝟏 𝒎−𝟏
𝒏 ∑𝒊=𝟏 𝒊𝒎
𝒏
𝒎 𝒎
∑ 𝒊 = ∑(−𝟏)𝒊−𝟏 𝒂𝒊,𝒎 ( 𝒊=𝟏
𝒊=𝟏
𝒏+𝒎−𝒊+𝟏 ) 𝒎−𝒊+𝟐