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Unformatted text preview: ∑ + = = = + = n i k k i m k k n m k k a a a 1 10 CMSC 250 Properties, con't. ● Distribution ∑ ∑ = = = n m k k n m k k ca a c 11 CMSC 250 Properties, con't. ● Distribution ∑ ∑ ∑ ∑ = = = = = m i j n j i n j j m i i b a b a 1 1 1 1 12 CMSC 250 Properties, con't. ● Interchanging order of summation ∑ ∑ ∑ ∑ = = = = = m i ij n j n j ij m i a a 1 1 1 1 13 CMSC 250 Nesting of sum/product notation ● Variations (same or different??): ∑ ∑ = = m i n j ij Y 1 2 1 ) ( ∑∑ = = m i n j ij Y 1 2 1 ) ( ∑∑ = = m i n j ij Y 1 1 2 14 CMSC 250 Factorial ● Product definition: n ! = ∏ i = n ( n1 )( n2) … 2 • 1 ● Recursive definition: 0! = 1 n ! = n ( n1)! ii i = 1 n...
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 Spring '08
 staff
 Summation, Bk, CMSC, Summations and Products

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