SummationHW-sol (2)

# SummationHW-sol (2) - n n n n n n n n n n n n n n n n n n n...

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Computer Science I – Spring 2011 Summation Homework: Due Wednesday 2/16/11, IN CLASS (Solutions) Evaluate the following sums: 1) 15379 4 * ) 1 10 100 ( 2 ) 1 10 100 )( 100 10 ( 3 4 3 ) 4 3 ( 100 10 100 10 100 10 = + + + + = + = + = = = i i i i i 2) ) 2 )( 5 2 ( 2 ) 4 2 )( 2 5 ( 2 5 + = + = = n n n n i n i 3) 4 3 4 1 3 4 1 3 ) 1 4 ( 2 2 ) 1 4 )( 4 ( n n n n n i n i n n i n i + = + = = = = 4) ) 1 ( 2 2 ) 1 ( 4 4 1 4 4 1 1 1 1 1 + = + = = = ∑ ∑ ∑∑ = = = = = n n n n i n i n i i j n i i j 5) 2058511 1710 2030100 30030 91 6 ) 1 18 )( 1 9 ( 9 6 6 ) 1 200 )( 1 100 ( 100 6 2 ) 1 10 100 )( 100 10 ( 6 91 ) 1 ( 6 1 12 12 1 ) 12 1 ( 100 10 100 10 1 100 10 100 10 100 10 1 = + + = + + + + + + + + = + + = + = + = = = = = = = i i i j i i i i j i i j j 6) 2 2 5 3 2 ) 1 )( 2 ( 2 ) 1 2 ( 2 2 2 1 2 1 2 1 + = + = = = = = n n n n n n i i i n i n i n n i 7) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 3 3 3 1 2 4 3 1 1 2 2 3 1 1 2 2 3 6 2 1 2 2 1 2 2 2 3 3 2 2 3 2 3 2 2 2 2 3 3 3 1 2 2 1 2 1 2 1 2 1 2 2 1 2 1 2 + + = + + = + + + = + + + = + + + = + = + = + = = = = + = + = + = n n n n n
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Unformatted text preview: n n n n n n n n n n n n n n n n n n n i i n i n i n i n i n i n i n n i n n i n n i 8) ( ) ( ) ( ) ( ) ( ) 2 1 3 2 1 2 1 6 2 1 6 2 1 6 6 2 3 2 2 1 1 1 1 1 1 + = + + = + = + = = ∑ ∑ ∑ ∑ ∑ ∑ = = = = = = n n n n n n i n n n n i j i ij n i n i n i n j n i n j...
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